It runs just fine for me, huh. Certainly not because of lack of google services.

Maybe graphene is doing some firewall things? KDE Connect needs some ports open (to the local lan) to talk

If you have a phone with custom ROM support, pretty easy. I’ve been running LineageOS without GAPPS for like 5 years now. Most stuff just works, but to be fair, I am not using any of the cool kids apps like google pay or android auto.