First, the tinyDB has no relation to the firebase authentication component.
It’s just that the login works. You go to the next screen when you login, as you have programmed, but you always login with the same google account.
If you choose another account, you don’t login with it, you login with the same one you used for the first time.
Try changing your google account and you’ll see that you can’t.
One way to verify it: use the Logout block to logout of your current google account. Then use the Google Account Picker component and select another google account. Put the image of the logged in user. You’ll see that the same user is always logged in.