Found this online, seems similar to your issue
My Nest WiFi router was showing a yellow light when I connected it, and I ended up just doing a factory reset on it. When I try to set up the router using Google Home, it finds the router fine, but as soon as I click the action to begin setting it up it says: DNS resolution failed for service: googlehomefoyer-pa.googleapis.com:443. It gives me nothing I can do beyond that, it just fails and exits the setup. I can't connect to any of the wifi settings in my existing Google home network because I can't connect to the network
Solved!
In case anyone happens to run into a similar issue in the future, it turned out to be some strange issue with the Google Home app specifically not being able to get any connection with anything. Even on cellular, just trying to log into another account from Google Home, it said it had connection. This persisted even after reinstalling the app.
So, I tried tethering to my wife's phone just to give it some other "network" to connect through, and all of a sudden I could get into the app, get to my old network settings and forget the network, basically reset the app. Once I did this, I was able to set up my Nest wifi router normally again.
