It’s also free in the Bitwarden app if you self-host with Vaultwarden. It’s only a paid feature if you’re using their hosting, and seemingly only so they can dangle it as a “premium” benefit.

Exactly. Doesn’t matter if they’re wired or wifi, or where they are, as long as they’re on the same network you’re fine.

If you’re only trying to use Jellyfin at home, you don’t need any reverse proxy or domain. All you need is for both devices to be on the same network, and for the Raspberry Pi to have a fixed internal IP address (through your router settings).

On the Shield, you just give the Jellyfin app that IP address and port number (10.0.0.X:8096) to connect and you’re good to go.

You should be fine on basically anything. I have a similar-spec machine running Arch with KDE and it’s rock solid.