Each device will need to be authorized with 2FA as a device being used by you. However, once done that should be it unless you completely reset the device.
Typically you should be presented with a place to enter a 2FA code. You weren't on really old equipment but that was if it was running iOS9, not 12.
Once you start getting messages like account details unavailable I would consult with Apple.
Contact Apple. Click here --> https://support.apple.com/choose-country-region Select your country, then a product. If you don't see one that handles your issue then keep experimenting with selections until you reach one that gets you a chat session or a telephone call and get the representative to redirect you.
or:
Contact Apple for support and service --> "See a list of Apple phone numbers around the world."
Click here --> https://support.apple.com/HT201232