On your LAN DNS server (say, pi-hole), you could add an A record for your Immich's domain name that points to the internal IP address so clients on your LAN would simply resolve the LAN IP instead of trying to do fancy NATing. Make sure your browser doesn't try to do DNS over HTTPS, which would skip your local dns.
Or you could run everything on a meshVPN like Tailnet. That way the (VPN) IP of the Immich server doesn't change and the Tailnet will route the traffic over your LAN when your clients are local.