No, it can run along anything, as long as you don’t conflict the IP space assigned to a VPN. It creates it’s own IP network space when running, so just don’t overlap with your other VPN software. Using it while at home is a bit wasteful on effort and power, but just use the Jellyfin LetsEncrypt setup and it’s the same thing.

You are missing a lot here. I think you’re confused on the difference between your LAN security, and how that fits into network connections. You don’t need an SSL cert to say that something is secure, that’s just one method of PUBLICLY securing something. Every connection on Tailscale is secure end-to-end, so if you run it on your Pi, any client that can connect to it is secured. No open ports, no lapses in security. The encryption happens between each client and the server. You’re secure.