The resolution to this issue is often making sure you have entered a credit card or other valid method of payment* even if you don't plan on needing to use it. The document 'If you can't remove your last payment method or use no payment method with your Apple ID' ( https://support.apple.com/HT203905 ) mentions, "if you're using an existing Apple ID with the App Store for the first time, you must provide payment information."
If there is an option to select "Review" or "Continue", select that and enter valid payment information if required. If there's problems doing this:
On a mobile device tap: Settings > [your name at the top] > Media & Purchases > View Account > Review Apple ID.
Alternatively this document explains how to 'Change, add, [review,] or remove Apple ID payment methods' on an Apple mobile device, a Mac, or a PC; click here --> https://support.apple.com/HT201266
More things to try in this 2018 post by Urquhart1244 marked Apple Recommended:
https://discussions.apple.com/thread/8434425?answerId=33542414022#33542414022
If you continue to have problems contact Official Apple Support - Select your region from the list and then your country from the pop-up window. If you do not see your country, see if there is an "other" listing for that region.
https://getsupport.apple.com/?caller=cups&PGF=PGF63005
*Payment methods that you can use with your Apple ID - https://support.apple.com/HT202631
I suggest you also send feedback to Apple about the looping issue. I see this posted at least daily and while there is a workaround, it's clearly a feature that is not working for everybody, or needs better explaining. Try entering your Apple ID email address and see if it then prompts for a password. If this works, please let me know, but according to this user it won't --> https://discussions.apple.com/thread/253412678?answerId=256387736022#256387736022.
Click on this link for Apple products feedback links --> http://www.apple.com/feedback/
