There are definitely services that do this. Something that comes to mind that’s related to Plex is nzb360, an Android app to connect all your torrent downloaders, usenet downloaders, sonarr/radarr, etc. It has an option for Local Connection Switching that, if enabled, will switch to using the local IP of your services when in the same LAN and go back to public IP when you’re not on the same LAN

Can I just ask, why not JellyFin?

Wouldn’t it be easier to right click -> copy link the image