Tailscale now supports buying Mullvad subscription through them and using it with their app. So it solves this issue, although the control you have over your Mullvad tunnel is less and it misses some advanced Mullvad features. Still probably good enough for most people.
I ended up going a different route by buying a VPS and hosting Caddy as reverse proxy. Then I only have my VPS and NAS on tailscale and other devices use the reverse proxy. This allows me to also share links to cloud files or other stuff I host with friends that are not on tailscale.
I just finished refining my Jellyfin setup. I use caddy as reverse proxy and use authelia as authentication in front of Jellyfin. This way only users logged in to authelia can access my Jellyfin. And there is an SSO plugin for jellyfin to avoid double login. The tricky part was getting apps to work.