I use Cloudflare tunnel to make it available outside the home network. I've set up two DNS names – one for accessing it directly in the local network, and and a second one that goes through the tunnel. The Immich mobile app supports internal/external connection settings – it uses the direct connection when connected to home wifi, and the tunnel when out and about.
For uploading photos taken with a camera I either use immich-go (https://github.com/simulot/immich-go) or upload them through the web UI. There's a "publish to Immich" plugin for Adobe Lightroom which was handy, but I've moved away from using Lightroom.