Have you tried directly using the Add to Library option?
Unable to save game analysis

That said I just tested and the updated game was added to the selected collection
Thanks for responding -- but my question was why doesn't it appear in https://www.chess.com/analysis/saved ? (What would happen if I didn't want to add it to a collection? Does it get saved anywhere?)
I went to game archive, did a game review of my game, made some annotations, and then hit "save"
I get a dialog box that asks me which library I want to save it in, which I can do. (Although I see that the green "save" button does *not* get grayed out)
*But* the game does not show up in my https://www.chess.com/analysis/saved -- and so if I do not save it in a library, all my annotations are gone.
Thoughts?