If a used phone says fully unlocked but H2O locked can I still use it with my AT

If it says "H20 locked", it's not fully unlocked.

Contact H20 (only that carrier can unlock it, if you are eligible) as per the these instructions:--> How to unlock your iPhone for use with a different carrier - Apple Support

Regards

Giulio

Is this showing under Settings > General > About > Carrier Lock?

AT&T has a support article that gives you options to see if you can unlock your phone and how to request it, but H2O is where you would have to go to see if they can unlock it. You may need a new SIM card, but it is really up to AT&T if they will help with the unlock.

The phone cannot be unlocked and locked at the same time. If the phone is locked to H20, you will not be able to use another carrier until the phone is unlocked by H20.