The message says PHP 8.0+ are supported but the table currently does not list 8.2. I assume the table should be updated?
Topic on Talk:Compatibility
You don't mention what version of MediaWiki you are running, but the release announcement for MediaWiki 1.35.10, 1.38.6 and 1.39.3 goes into some detail about this. In summary, PHP 8.0 and 8.1 should work without major issues, though support for 8.2 is less mature.
See https://lists.wikimedia.org/hyperkitty/list/mediawiki-announce@lists.wikimedia.org/thread/6UQBHI5FWLATD7QO7DI4YS54U7XSSLAN/ for the release announcement.
I did not mention it because I am not running it. :)
The specific question was asked because the documentation is apparently inconsistent. Either MW supports 8.0+ and so the table should be amended, or it doesn't and the note should be just a bit more specific about the expected level of support for 8.2. Based on the documentation I've seen, including the 1.39 patch notes, 8.2 is actively supported, so that's why one might expect the table to include 8.2 rather than the note be adjusted.