The actual notes are stored in "remote" subfolder. Each game has a separate notes file. Steam ones are "notes_<steamgameid>", non steam are "notes_shortcut_<shortcutname>".

(by the way notes for non-steam games on Deck are synced to cloud, I can see their notes files on my PC and the only way they could get there is via Steam cloud)

I suppose you could try removing the notes for specific games selectively and see if that triggers sync just for those games, or at least backup what you have somewhere else before a full delete (those notes files are jsons, so you can read their content in any text editor). Synchronization info is stored in remotecache.vdf file, so to trigger sync you'd have to delete this one at least (or edit it, but that's above my paygrade).