What is this AppleTV box running TS that you speak of? Sounds awesome.
Doesn’t have to be an apple box either. A raspberry pi is what I’m using. I’m in the exact same situation, living in one country temporarily but citizen of another, and I have an exit point in my home country at my parents place on a raspberry pi. Basically any computer will work.
Check out the instructions from Tailscale: https://tailscale.com/kb/1280/appletv