For me this involves going up into my attic and I can’t do that if I’m remote and currently I’m having to do it weekly. They need to resolve their networking deficiencies.
I also have this setup, Google Nest Wifi mesh network with two nodes and the devices shows “no wifi”. Within the thermostat, selecting “Settings → Device Info” will show “strong signal” and a correct IP address, yet the symbol shows “no wifi” and app shows “device offline”. Resetting it (turning furnace off) sometimes causes it to return to service.
My guess is it is not mesh-friendly.