syncthing also relies on a web server for device discovery, it’s just that you’re probably using someone else’s server instead of hosting your own.
Correct me if I’m wrong, but I also think that Vaultwarden itself doesn’t have access to the unencrypted password database. In that sense it’s E2EE similar to KeePass, the only difference being that KeePass is a desktop app and Vaultwarden a web app.