For Android, we have no issues handling the Publisher login and order placement through web view which opens in our app. But for our iOS build when the user tries to log in to the publisher, it asks for credentials and then sends the user to the 2FA page. Still, when they enter the 2FA(TOTP), it returns to the login page with an error at the bottom 'Please complete the login before doing 2FA verification.
You may try your luck with offsite basket execution, but not sure if it works or not.