I've finally used "prompt=select_account" instead : in case the user was already logged in his personal gmail account, he was DIRECTLY leaded to a 403 error without a chance to login to another account. Now each time he clicks on "google login" button on the front page of Moodle, he's redirected to a "select an account" screen.
Using "prompt=consent" will work but the project in google console has to be set to "public" which was a problem for me since I've added Google Drive in the scope, I didn't want to go thru Google Project validation process.
Using "prompt=consent" will work but the project in google console has to be set to "public" which was a problem for me since I've added Google Drive in the scope, I didn't want to go thru Google Project validation process.