What your trying to do is a big overkill if you want only one device to connect to a VPN.
Your VPN installed on your raspberry pi should have a “local network sharing” option. Based on some blogs mullvad had some issues with hostname and network shares (as of 07/2022) and you should try to connect via IP address if you’re having trouble.
Local network sharing only works on the same subnet (IP address of your computer, Pi, and TV should have the first 3 parts of the IP match, ex: 192.168.4.xxx not 192.168.x.xxx).
If you’re trying to SSH to the Pi when not connected to the same network it’s going to be much more difficult.