In most reputable sources, overleaf indeed implies turning the paper over. Still, it is not uncommon for books to engage in the same sort of 'abuse' as you do and use overleaf when they mean opposite. Certainly there are cases where this can lead to confusion, but my guess is that usually the meaning will be clear from the context. As far as alternatives to opposite, a common one is the facing page (as user alwayslearning has said in their answer to your question). In fact, facing might actually be used more often than opposite in this context, if general dictionaries are to be believed.
I don't know of a universal replacement for this page. Personally, I use designations such as the previous paragraph, the sentence following Eq. (12), etc. These are admittedly not elegant, but they are more precise than this page and, moreover, they remain valid if pagination is changed.
I should acknowledge that I found at least one reputable source, A Handbook to Literary Research, that breaks Rule 1 and uses overleaf instead of opposite on a verso (left) page to refer to the following recto (right) page (see pp. 18-19).
The sources I will present below use the words overleaf and opposite page according to the following rules:
The rules in words:
Rule 1. The text on a verso (left) page refers to the items on the immediately following recto (right) page as being on the opposite page.
Rule 2. Conversely, the text on a recto (right) page refers to the items on the immediately preceding verso (left) page also as being on the opposite page.
Rule 3. A recto (right) page refers to the items on the immediately following verso (left) page as being overleaf. (This is obvious, as these two pages are in fact the two sides of the same sheet).
Rule 4. A verso (left) page refers to the items on the next-in-sequence verso (left) page as being overleaf. (This is perhaps a surprise; it says that the word overleaf denotes the exact same page regardless of whether the word appears in the text on a verso page, or in the text on the recto page that immediately follows the verso page. One might have thought that the word would instead refer to the recto page immediately preceding the present verso page.)
One note on Rule 4: in both reputable sources that use it below, it is used very soon after the sources use Rule 1 on the same page—in other words, the text on a verso page (e.g. p. 66) first refers to the opposite (i.e the very next recto) page (in this example, p. 67), and then uses overleaf to refer to the next verso page (p. 68). It is pages 67 and 68 that are two sides of the same physical leaf. It is possible that, when these sources say overleaf in that context, they are using a kind of ellipsis, and are actually saying overleaf from the page we just referred to rather than from the present page.
Some books generalize Rule 4 and use overleaf to refer, from a verso page, even to objects several pages ahead of the facing recto page. For example, on p. 158 of Field Sketching and the Experience of Landscape, Figure 7.6 on pp. 160-161 is referred to overleaf, as is Figure 7.7 on p. 162, Figure 7.8 on p. 163, Figure 7.9 on p. 164, and Table 7.1 on p. 165. Again, all these references are from p. 158.
Evidence for these rules from reputable sources
I will give details in the last section of my answer. For now, here is a summary of the findings.
All fourteen major dictionaries I looked at list overleaf as an adverb with the meaning on the other side of a page (or sheet). Oxford English Dictionary says it can also be an adjective with a corresponding meaning (so that an overleaf table is a table that's overleaf), though it marks this usage as rare. This was also the finding of user alwayslearning: dictionaries are unanimous that overleaf does not mean on the facing page, but rather on a page that will require you to turn the leaf over to see.
All this is consistent with Rule 3 above. However, none of the dictionaries, in their entry for overleaf, suggest anything like Rule 4 above. And yet, as we will see below, Rule 4 is frequently used in reputable books.
As far as facing/opposite page, four dictionaries explicitly mention facing as an adjective in the context of Rule 1 and Rule 2.
The remaining ten do not record this usage. However, the four dictionaries that do are among the most famous ones, including the Oxford English Dictionary, Merriam-Webster, and Lexico (formerly Oxford Dictionaries). These last three also say, in their entries for facing, that opposite is an equivalent word in that context.
Interestingly, only two dictionaries suggest, in their entries for opposite, that opposite can be used in the sense of Rule 1 and Rule 2—and it's not any of the above three, but rather Cambridge and Macmillan.
None of the dictionaries makes it explicit whether it is endorsing both Rule 1 and Rule 2, or just one of these rules. However, the way the definitions are written, it seems likely that they are endorsing both rules.
Usage in reputable sources
Consider the book Getting it Right with Type: The Dos and Don'ts of Typography.
Rule 1 and Rule 4 are illustrated on p. 66, where it says that A good sixteen microtypographic errors are hidden in the example on the opposite page, and that search for mistakes is helped overleaf. And indeed, on p. 67 is some dummy text (in accordance with Rule 1), while on p. 68 we find the 'solution' (in accordance with Rule 4), with the errors highlighted.
Rule 3 is illustrated on p. 31, where it is stated that The critical letter combinations in the various typefaces are compared overleaf. According to Rule 3, this should mean p. 32, and it is indeed so.
Unfortunately, there is no instance of Rule 2 in this book, at least not in what's accessible on google books.
The same three rules (Rule 1, Rule 3, and Rule 4) are used in the book Some Notes on Books and Printing: A Guide for Authors and Others.
Consider next the book The Oxford Shakespeare: Timon of Athens, in particular this sentence on p. 122:
Hence one refers to the page that appears overleaf from K2 and opposite K3 as K2v.
This illustrates Rule 2 and Rule 3, as will become clear once I explain what K2, K2v, and K3 are. They are denotations of pages in a book (a folio) from Shakespeare's time. A folio is put together from quires, each of which is a gathering of three physical sheets which are then folded in half. All this is best presented visually, as in the following illustration. It shows how the plays Julius Ceasar and Macbeth are assembled in the First Folio (which is a famous collection of Shakespeare's plays, published in 1623):
(The illustration is from here, though I added the underbraces, the red arrows, and the corresponding explanations. The actual image link is this).
You can see scans of these actual pages from the First Folio here.
So, a quire consists of three physical sheets, which are then folded in half to produce six leaves. Each leaf has two sides, and thus each quire contains 12 numbered pages. However, at the time, folios didn't have consistent page numbers. But the printers nevertheless needed to be able to properly identify the physical sheets. Their solution was to put one distinctive mark, called a signature, on each physical sheet. In the First Folio, for example, the marks are placed in the lower right corner of each physical sheet. The first sheet in a quire might get marked as 'kk', the second as 'kk2', and the third as 'kk3'. Then the sheets in the next quire get marks 'll', 'll2', and 'll3'; the sheets in the quire after that get 'mm', 'mm2', and 'mm3', etc. As a result, as should be clear if you look at the illustration above, once the physical sheets are printed, folded in half, and assembled, these signatures will appear on the first three recto pages of each quire. (In a book written in a left-to-right script, a page is called recto if, when we are reading that page, it is on the right-hand side of the book; if it's on the left-hand side, it's called a verso.) The last three recto pages in a quire have no signature, but we can still say, for instance, that the first recto page following 'kk3' is 'kk4', the one after that is 'kk5', and the final one for that quire is 'kk6'. So now we have an unambiguous way to refer to all the recto pages in a folio. Notice that each leaf has a recto and verso side, and we just saw how to identify the recto side. Then, to refer to the verso side of the same leaf, we add a subscript 'v'. For example, the very first page in the quire shown on the left in the illustration above is a recto with signature 'kk' (p. 109). The following page (p. 110) is a verso on the same leaf as 'kk', so we refer to it as 'kkv'. The order of the pages is thus kk, kkv, kk2, kk2v, kk3, kk3v, kk4, kk4v, …, ll, llv, ll2, ll2v, etc. We can say that the letters 'kk' designate the quire, the numbers† 1-6 designate the leaf, and the 'v' designates the side of the leaf (verso if there is a 'v', recto if there isn't). (See here.)
†Where '1' is not actually written.
With all this mind, look again at the sentence from The Oxford Shakespeare: Timon of Athens. It says (translated to the example from the illustration above) that kk2v is opposite kk3 (which is in accordance with Rule 2), and that kk2v is overleaf from kk2 (which is in accordance with Rule 3).
Here are several additional sources illustrating the various rules.
Near the bottom of p. 53 (which is recto) of Basics Design 02: Layout, the words (opposite, top) and example shown opposite refer to the items on the previous page (p. 52), which is verso, in accordance with Rule 2. You can see that pp. 52 and 53 are a verso-recto pair by the way the book displays page numbers: for both verso and recto, it displays them in the upper-right corner of recto (so here on p. 53), where '52' (which is actually the page number of the previous page) is in a font of regular weight while '53' (the page number of the current page) is in boldface.
On p. 35 of the textbook Principles Of Biopsychology, which is a recto, it is stated that an illustration of the spinal cord is given on the opposite page, and indeed there is such an illustration on p. 34, which is a verso. This is in accordance with Rule 2. The multiple usages of overleaf on p. 35 all refer to the illustration on p. 36, in accordance with Rule 3.
On p. 339 of New Theatre Quarterly 76, Volume 19, certain items are referred to as being on the opposite page, namely 'a dancer carrying the kāpā' at the top, and 'dancers executing subdued movement' at the bottom. And photos of both of these are found respectively at the top and the bottom of p. 338, in accordance with Rule 2. (I'll admit that I don't know what the word overleaf on p. 338 refers to. There doesn't seem to be any images corresponding to the stated description either on p. 340, as Rule 4 would demand, or on p. 337, as the 'common sense' interpretation would suggest.)
Rule 3 is given in Dictionary for Library and Information Science as follows:
overleaf On the other side of the leaf, a term used in captions to refer to full-page illustration on the reverse side of the same leaf.
This is a bit narrower sense of overleaf than what we've seen above.
General dictionaries—in detail
Entries for opposite
Only two general dictionaries had an entry for opposite that explicitly mentioned the context of facing pages, and even then, in neither case was it part of the definition, but it was rather one of the examples of usage:
In the Cambridge Dictionary:
opposite adjective (FACING)
being in a position on the other side; facing:
The map on the opposite page shows where these birds commonly breed.
opposite adjective [usually before noun]
2 across from or on the other side of someone or something
A picture on the opposite page caught her attention.
No other general dictionary had even as much, and I looked at quite a few:
the Oxford English Dictionary,
Lexico (formerly Oxford Dictionaries),
American Heritage Dictionary,
Webster's New World College Dictionary, Fifth Edition (via Yourdictionary.com),
Random House Unabridged Dictionary (via Infoplease),
Webster's 1913 Dictionary,
Entries for facing
Dictionaries seem to regard this word as better suited for referring to pages in a book, although they typically, in their entry for facing, also list opposite as an equivalent.
Oxford English Dictionary, in its entry for facing as an adjective, records this meaning:
- That faces or is positioned so as to face; that is opposite to, esp. in facing page.
1 : located directly across from something : opposite
// an illustration on the facing page
Lexico (formerly Oxford Dictionaries) has
facing adjective [attributive]
Positioned so as to face.
‘two facing pages’
Lexico typically gives many examples of usage from its corpus, and in this case as many as five use facing in the context of facing pages. Here are two of them:
‘Indeed, Sheth has arranged the images in such a way that you see two different worlds on facing pages.’
‘The portentous first page of text does not mention the artist, whose engraved image floats within an oval frame on the facing page.’
Finally, Vocabulary.com records facing pages as a compound noun, with the (hopelessly circular) definition two facing pages of a book or other publication.
Interestingly, the other dictionaries I looked at didn't record the use of facing as an adjective (American Heritage Dictionary, Macmillan, Collins, Cambridge, Wiktionary, Webster's New World College Dictionary, Fifth Edition (via Yourdictionary.com), Random House Unabridged Dictionary (via Infoplease), Webster's 1913 Dictionary, Dictionary.com,
Entries for overleaf
Oxford English Dictionary:
overleaf, adv. and adj.
On the other side of the page or leaf.
See the table, overleaf, for more detailed information.
Of a piece of text: written or printed on the other side of the page or leaf. rare.
The Bank offers over 200 services, so the overleaf list is of necessity brief.
: on the other side of a leaf (as of a book)
//find the answers overleaf
English Language Learners Definition of overleaf
chiefly British : on the other side of the page
Overleaf is used in books and magazines to say that something is on the other side of the page you are reading.
Random House Unabridged Dictionary (via Infoplease)
on the other side of the page or sheet.
The definitions in the other dictionaries are very similar to the ones above (Lexico (formerly Oxford Dictionaries), American Heritage Dictionary, Macmillan, Vocabulary.com, Cambridge,
Webster's New World College Dictionary, Fifth Edition (via Yourdictionary.com),
Webster's 1913 Dictionary,