I have Tailscale directly installed on the host and I don’t use Mullvad so I haven’t tried that setup myself.
Looks like you would need to set the TS_EXTRA_ARGS
environment variable in your container to --exit-node= --exit-node-allow-lan-access=true
with the exit node name or ip of the Mullvad node. I haven’t tried this myself though.
I haven’t tried it myself but LOOT has a native Linux version on Flathub. https://flathub.org/apps/io.github.loot.loot