I was just in your exact Situation with my Jellyfin home server. I was using Tailscale for a while, but ran into a problem: my new server is really bad at encoding, so I can only use direct play, which uses more bandwidth than the tail scale relay servers can give.
The problem with tail scale is, I basically only ever use the relay servers because my home is cgnat and most of the time when I want to stream outside of home I am on mobile data with cgnat or at college (restrictive firewall).
My solution which I implemented last weekend was to buy the cheapest VPS I could get from my trusted provider and harden it and install nginx proxy manager and tailscale. With that, I can make a direct (no relay server) connection to my home server and proxy Jellyfin to a public domain.
~~I am still figuring out how to secure Jellyfin, but I have also seen some comments that Jellyfin is secure by default and therefore ok to have exposed.~~
Actually no, it is insecure, do not expose it to the internet. I will be adding separate authentication to access it via proxy.