I’ve always wanted to do this however do I understand it correctly that I need to host headscale on a vps server that is not in my tailnet/home network?

Use the jellyfin kodi addon works very smoothly. I’ve been using it for two years and love it. I replaced all my chromecasts with kodi. It even has the approval of my wife.

Firedragon on desktop( I use garuda Linux) and Mull on android

If you try to browse to the tailscale website does it work?

If it does you could setup tailscale with an exit node at your house and tunnel your connection that way? Everything would then be coming from your home internet. I have had good success with tailscale being able to punch a hole through some pretty filtered firewalls.