My understanding is that the part of speech of participles is somewhat controversial. Here is a post I made earlier about it with some links to the relevant literature that I know of: Is “running” a gerund or a participial adjective? Basically, some people think "participles" can be analyzed as verbs (in some cases), while other people (possibly a minority) think it is appropriate to analyze participles as adjectives in all cases.
However, as far as I know, there is agreement that words with the form of participles are at least sometimes adjectives and not verbs. (I said "words with the form of participles" because I have the impression that some writers reserve the term "participle" for words that they classify as verb forms, but I'm not totally sure about this.)
In particular, people seem to agree that a word like "sweetened" or "noticed" would be an adjective in certain situations where it is used gradably; e.g. "the tea didn't taste very sweetened" or "the tea seemed sweetened". (BillJ's answer to the linked question lays out the relevant tests more concisely and accurately than mine.) It seems relatively difficult to me to do this for "noticed": "very noticed" and "seemed noticed" sound a bit awkward. So maybe some people would argue that "noticed" is not well-established as an adjective. (However, some verbs of this type seem to work better with "noticed" than others ... "I don't feel noticed" sounds fairly acceptable to me.)
(While I'm not entirely convinced, another test that some people think demonstrates adjective-hood is if the word can be used attributively before a noun. "Sweetened" passes this test just as well—we can speak of "sweetened water" or "sweetened coffee"—while it's hard for me to think of a natural way to use "noticed" attributively. The Google Ngram Viewer indicates some use of "the noticed fact(s)" and "the noticed parts").
Un- prefixation and part of speech
To get to your specific question: it has been suggested that un- prefixation (with the meaning of negation rather than reversal) is a definite indicator of adjective-hood. The literature where I found this mentioned: Laczkó (2001) (citing Bresnan, unpublished), Meltzer.
So I think many people would agree that "unsweetened" and "unnoticed" are adjectives.
The only possible counter-argument I am aware of is that apparently, some people view any word with the form of a past participle followed by a "by" phrase as verbal rather than adjectival. This criterion is described in the article "Participial Adjectives" on the Internet Grammar of English. However, I think this resource is mistaken, and when I posted an answer saying that on Linguistics SE, I didn't encounter any disagreement. So I would say that even phrases like "unsweetened by any illusions" or "unnoticed by the public" are adjectival, not verbal. They do pass the "seemed"-type test ("seemed unsweetened by any illusions" and "seemed unnoticed by the public" both sound acceptable to me).
Of course, not all words with the form of past participles can be prefixed with un-. Past participles based on verbs that can only be intransitive, and that aren't used to describe the subject (like "fallen"), seem unlikely candidates to me. Specific examples that don't seem possible to me: *unbelonged, *undied, *unexisted, *unlaughed.
This is a side point, but one fact that I found surprising is that the adjective prefix un- and the verb prefix un- have different ultimate origins (as described in Bea Bonmot's answer here). The adjective prefix is the familiar Indo-European negative prefix cognate to Latin in- and Greek a(n)-. The verb prefix is actually cognate to German ent-.