Aha, ok, so it's using pipewire when logged in locally, and it can't find it when using it remotely.
Can you try logging in via ssh again and checking if there's a /run/user/$UID/pipewire-0 (or other pipewire-<NUMBER> sockets)?
If there isn't, that means your pipewire service isn't running, you can try starting it with systemctl --user start pipewire wireplumber. You may need a loginctl enable-linger $USER and a re-login for that to work. You can also do systemctl --user enable pipewire wireplumber so that it auto-starts them whenever you log in, if that's not already the case.
If/once that socket is there, you may need to export XDG_RUNTIME_DIR=/run/user/$uid so that mpv can find the socket. You should probably do that in your .profile so it's set automatically.