Thanks again.
Our developer found the problem.
Maybe it will help others too.
It looks like after putting the password as expected and then the 2fa code too, it goes back automatically to the password page again and submit it again. If there is an auto filling like last pass – it can auto fill it with wrong password – overriding the original filled password used before the enter of the 2fa code, and that’s if the saved password there – is not the current one.
So the solution was to make sure the password is saved up to date in Last pass or the google password manager, or to turn off the auto filling at all.