The ability to annotate archived material on the Internet Archive with Hypothes.is is definitely possible, and I do it from time to time. I’m not sure which browser or annotation tool (via, browser extensions, other) you’re using, but it’s possible that one or more combinations may have issues allowing you to do it or not. The standard browser extension on Chrome has worked well for me in the past.
Hypothes.is has methods for establishing document equivalency which archive.org apparently conforms. I did an academic experiment a few years back with an NYT article about books where you’ll see equivalent annotations on the original, the archived version, and a copy on my own site that has a rel="canonical" link back to the original as well:

https://www.nytimes.com/2017/01/16/books/obamas-secret-to-surviving-the-white-house-years-books.html
https://web.archive.org/web/20170119220705/https://www.nytimes.com/2017/01/16/books/obamas-secret-to-surviving-the-white-house-years-books.html
https://boffosocko.com/2017/01/19/obamas-secret-to-surviving-the-white-house-years-books-the-new-york-times/

I don’t recommend doing the rel-canonical trick on your own site frequently as I have noticed a bug, which I don’t think has been fixed.
The careful technologist with one tool or another, will see that I and a couple others have been occasionally delving into the archive and annotating Manfred Kuehn’s work. (I see at least one annotation from 2016, which was probably native on his original site before it was shut down in 2018.) I’ve found some great gems and leads into some historical work from his old site. In particular, he’s got some translations from German texts that I haven’t seen in other places.