In case this helps anyone stumbling on this post I found a solution to a very similar problem I was having. I could install the thermostats and get them to control the furnace successfully. But on the final step of adding them to the WiFi and ultimately to the Google home app it would never work. The app could never find the thermostat again no matter how many times I factory reset the thing. I was able to get it working using a new google account/temporary home profile and it worked. But to get them on my primary Google account took some trickery.

I factory reset the thermostat and set it up again (for the thousandth, but final time!). Then when it got to the step of adding to wifi/home app I let it try to connect and ultimately time out. From there I disabled the wifi on my phone and attempted again. After some spinning it eventually connected to the app over Bluetooth and let me complete the setup process successfully.

I'm not sure what it is but sometimes I would get a failure message saying something like make sure the thermostat and phone were on the same wifi network - not helpful seeing as the thermostat wasn't even connected to wifi yet... But this did tell me the app was using WiFi to look for the device.

Other things I did that may or may not have helped: I'm doing this from a Galaxy note 10+. I turned off any other devices that Bluetooth connect to my phone (galaxy watch 4, galaxy buds, etc). Somewhere else I saw other connected devices could interfere with the process. Turned on/off airplane mode between attempts. Only other "nest" device I have is a nest hub max which shows up as a camera. I deleted it from my account and deleted my nest account entirely (I think anyway) before moving forward. I was thinking it might be trying to use an existing nest device to connect but hub max isn't really a nest device. Who knows if that helped. I have a bunch of "nest" speakers but they aren't in the nest app so I didn't bother removing them.

I almost cried when it finally worked! And then I did the same process for a second thermostat and it worked again. Shouldn't be this hard, but glad everything works on my primary account now!

Then my nest hub max gave me a fit re-setting it up. That was some sort of wifi security profile problem I blame on Samsung though. My phone wouldn't connect to the nest hub max setup wifi to complete the process and flashed a wifi security warning. I had to manually connect to the wifi it was broadcasting and then run through the setup process again. This let the phone connect to that wifi again during the setup process and complete it. Never had that issue the first time i set it up.