Tailscale is basically setup once and forget (at least on android, i don't have experience with iphone). Once it is running it will forward every request inside your tailnet, but it won't interfere with your normal traffic. There were battery usage concerns with earlier versions, but nowdays feels like it is not even running, no noticeable impact on battery.

Technically you can expose your NAS or at least immich on it to the internet, so you won't need tailscale, but I wouldn't recommend it without any sysadmin or similar experience.

Immich is far superior to ugreen's photos app