It does for my setup. I’m on a not too crazy install of Arch with KDE for my DE and I have discord installed with flatpak. It’s been at least 3 months with no issues for me.

I don’t have a use case, so I can’t test. This looks promising, though:

Shared Progress Across Copies: Progress is now stored against the Calibre book rather than the file checksum, so different copies/formats of the same book on different devices stay in sync. (PR #1225)