Two-Factor authentication broken for google account in new app, locked out of SmartThings

After I sign in to the app using “Continue with Google”, I am then prompted for my gmail password as part of “two factor authentication”. Of course, Samsung doesn’t know my gmail password. I entered it anyway, and it fails.

This is on a Samsung Galaxy Tab A 10.1 2019 tablet. I’ve previously logged in on my android phone and it’s worked. I’m too scared to log out and in again on my phone in case I can’t get back in.

Registering a stand-alone account with Samsung isn’t an option, as I have 170 devices over two locations connected on the account.

TL;DR - After signing in with “Connect with Google”, why does Samsung prompt me for gmail password (screenshot below), which it can’t verify?