> I don't know how the app will behave when it can't reach the server half the time
Immich has automatic URL switching, so it detects which network it's on and select between the internal and external URLs. When I'm not on my home WiFi it switches to the Tailscale URL. Tailscale must be connected for this to work obviously.
If you run DNS at home (even just dnsmasq) and you bridge your home 192.whatever to tailscale, you can make the same domain name resolve both at home and via tailscale.