I'm on 13.2.3 and a lot of the worst things seem to be fixed. That said, I still find some of the design changes odd and unintuitive (e.g. new editing gestures, new Music/Mail layouts). Mail is still infuriatingly slow at almost everything. I think you could probably call it stable (for my usage).

Note that there were also some... "interesting" iCloud sync design choices. You need to upgrade all devices (including macOS) to be sure of proper syncing in some cases, with odd behaviour ensuing if you don't.

iOS 13 and Catalina have been OK for me, XCode on the other hand is a hot mess.