Why does turbo tax limit my Arizona tax credit to $200 when that credit is over $400? I donated $400 to a qualifying charity, I deleted it from my federal return.

The AZ tax credit for donations to a qualifying charitable organization is a non-refundable tax credit.  That means the amount of credit used cannot exceed your AZ tax liability.  The unused part of these non-refundable credits is carried over to the next tax year.  So once your tax liability is reduced to zero by your "available non-refundable credit" amounts the rest is not used and carried over to become available next year.  

Your "available non-refundable credit" amount is equal to the current year qualified donation limited by the law ($421 for single taxpayers for 2023, for example) plus any credit amount carried over from the previous year.