Will migrating my Nest to using a Google Account mess up the HA integration?

Today my wife changed the Nest mode with the iOS app from Heat to Automatic.

RANT BEGIN
I absolutely hate Automatic mode. Something infuriates me when the outside temperature is -12F° and I suddenly feel a cold blast of air cross my forehead. And I go completely ballistic when the heat comes on and it’s 95° outside with 88% R.H. If you’re hot or cold, adjust the thermostat temperature setting. I’d rather you open the window instead of running the equipment in the season’s opposing operating mode.

Automatic mode should be outlawed.
RANT END

So after suspecting that the Mrs once again turned on Automatic mode, for some reason I tried using the iOS Nest app instead of using HA.

I know that Google has been jerkwads by making third party access to the Nest go bye bye. I guess I’m lucky that I integrated Nest with HA a few years ago, because I can still control my Nest with HA.

Today when I tried opening the Nest app, it’s only giving me the option of signing in with Google. I’m afraid to try this or grant permissions for the prompt “Nest wants to access your Google Account”. If I allow this, will I lose the ability to control the thermostat with HA?

Did you ever end up migrating your nest account? If so does it still work with HA. Was it seemless or did it take a lot of work to get it working again?

I still haven’t migrated.