Thanks for reaching out. I'm sorry to hear that you're having an issue with pairing your Nest Thermostat to your Google Home app. I'd love to know more about this and I have a few questions:
Looking forward to your response.
The thermostat is connected to the same Wi-Fi network as my other Nest devices and my phone. It controls my HVAC system with no problem from the thermostat directly. There is no error given in the home app other than the device cannot connect and may need a factory reset. I already did two full factory resets with it still not being able to connect. The internal battery is charged.