Tailscale was updated with direct support for Mullvad, but since you already have Proton I'm guessing you wouldn't want to switch.
If you're using containers, you can have one container with your VPN and route traffic from specific containers through the VPN container. You can then have tailscale on the host system.
There's a quick guide on setting up the VPN part here. Tailscaile you set up normally.
I haven't used that feature so I can't really say, but I don't see how it would affect it. You're not modifying anything on the tailscale side and you're not adding nodes to your tailnet, you only have the same one for the host system.