Yes, the best feature about KeePassXC is this ability to do your own syncing. I work at a Fortune 500 where they block every syncing service except OneDrive, so that's what I have to use.
You might be able to get Syncthing to work if you use a relay server listening on port 443, it would depend on their firewall.
Unfortunately Syncthing does not work on iOS, so it's not a fully cross platform solution.
I am not a fan of Syncthing. I do not want a web UI, and there UI is by default unsafe and needs to be disabled or secured anyway. I do not like their config format either.
Same here... really well built products that just work!.
I prefer KeeWeb for the UI, but Syncthing is great.