Yep I was totally wrong up above; **tailscale** absolutely works on local lan! It's the app that punches through routers no matter where your device goes. It's the whoke point, and it works great!

(I had posted about headscale today too in another note, which does need a public IP, so I got confused)

The tailscale documentation on their website is very good, they have plenty of use-case tutorials.