For me, the problem was not the annoying notifications — I just turned off Google Assistant. (In the Google app: Settings > Google Assistant > Assistant > Phone) The problem was that it keeps begging you to turn it back on. But anyway, the method of getting rid of Google is the same:
Uninstalling all updates for the Google app by clicking "uninstall" in the Play Store (rolling back to the version that comes with the system) and turning off autoupdates for it in Google Play seems to help.
But it sure has its problems. Sooner or later, the newest version of Google app will ship with all phones, and rolling back won't help.
And then, you will just have to google (haha) how to uninstall apps with ADB/Fastboot and just uninstall google app altogether, if you're comfortable doing that. There is a utility for xiaomi phones called "Xiaomi ADB/Fastboot Tools". It can remove any app and requires no root, but you will need to enable usb debugging. Even if it doesn't work for non-xiaomi phones straightaway, I'm pretty sure it can be made to work with them, or you can just use command line to do the same things.
I am sure that removing Google isn't harmful to your device in any way. If you're addicted to Google search, you can just use Chrome's search bar widget. And it seems that Google's two-factor authentication for your account is a system-integrated thingie that doesn't depend on the Google app at all. But nevertheless, if you're going to remove Google app from your phone, I DO NOT guarantee that you won't brick your phone and/or two-factor authentication by doing so, and you should do your own research. It's pretty unlikely that you'll brick it, though.