I received a 1099-MISC from the Minnesota Department of Revenue in the amount of $780 late in 2023. Where do I add this info?

What is it for?  A refund?

Yes a refund check from the State, i see the spot to add it to TurboTax but it wants a "Tax Year of Refund" and i cannot choose 2023.  2022 or earlier are the only options.

It appears you are attempting to add the amount as a "State/Local Tax Refund" form 1099-G.  This rebate amount on a form 1099-Misc needs to be entered in the "Other Common Income" dropdown where you will find the form 1099-Misc topic.  This specific rebate is taxable  at the federal level.  

Then, in the MN state interview you will enter the same amount in the "MN Tax Rebate" box when asked. this will subtract the amount from MN state taxes.  

You are right, i was doing the fields per Turbotax but going selecting the sections myself i was able to bypass the 1099-G and put it in the correct spot.