The use of "meta" as a standalone adjective is often considered to have started with Gödel, Escher, Bach, published in 1979. The book, and Hofstadter's subsequent column in Scientific American, almost certainly popularized the usage as a prefix, although there might have been something in the zeitgeist, because the term "meta-analysis" was unrelatedly introduced by Gene Glass in 1976 . The standalone usage was still not standard in 1988, when an article on the "meta-" fad appeared in The New Republic , but was clearly anticipated:
According to David Justice, editor for pronunciation and etymology at the Merriam-Webster Dictionary, “meta” currently is “the fashionable prefix.” He predicts that, like “retro”—whose use solely as a prefix, is so, well, retro—“meta” could become independent from other words, as in, “Wow, this sentence is so meta.” If so, you heard it from me first.
The use of the prefix "meta-" to mean higher-order or self-referential is older, but not all that much older. It was essentially not productive before the 20th century, and had no relationship to self-reference or recursion. To the extent "meta-" was used, it simply meant "after" or "beside." Metaphysics was simply the volume that came after Aristotle's Physics.
The point is, "meta" is a neologism, but one with a pretty good pedigree. Gödel, Escher, Bach won a Pulitzer.
As for modern usage:
- "Meta," as a stand-alone adjective meaning self-referential, recursive, or higher-order, is widely understood and appears in dictionaries. However, it is considered informal. In formal writing, the more precise term, such as "self-referential," "recursive," or "higher-order," is preferred. If you're looking for an adjective that unmistakably means "meta-" in the modern sense, these are your choices.
- "Meta," meaning mind-bending, philosophical, deep, or trippy, is colloquial
and nonstandard, and is not always accepted.
- "Meta," meaning optimal or "part of the metagame," is internet slang and many people will not understand it. Even among the gaming communities that use this sense of the word, its use to mean "optimal" is often controversial, and may trigger arguments.
 See, for example, Keith O'Rourke, "An historical perspective on meta-analysis: dealing quantitatively with varying study results," https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2121629/
 Noam Cohen, "Meta-Musings," https://newrepublic.com/article/164217/meta-musings