Google drive in files not working

As indicated in your first screenshot, before Google Drive will be accessible within the Files App, you must first open the Google Drive App - and sign-in to your Google account.

After signing-in (“authenticating”), you should be able to access Google Drive from the native Files App.

Your first screenshot suggests otherwise.

Removing the Google Drive App from your iPad - and then performing a forced-restart before reinstalling the App - may resolve the problem.

Force restart iPad (models with Face ID or with Touch ID in the top button)

If your iPad doesn’t have the Home button, do the following:

1. Press and quickly release the volume button nearest to the top button.
2. Press and quickly release the volume button farthest from the top button.
3. Press and hold the top button.
4. When the Apple logo appears, release the top button.

Force restart iPad (models with the Home button)

Press and hold the top button and the Home button at the same time. When the Apple logo appears, release both buttons.

You are very welcome.