Do I claim sales tax paid to register my car in New York State as a credit on my Indiana tax return for 2023?

Asked and answered.

https://ttlc.intuit.com/community/state-taxes/discussion/is-the-credit-for-4-reciprocal-sales-tax-paid-to-new-york-state-for-registering-a-vehicle-purchased/00/3082476

When you bought the car in Indiana in 2019, you pay sales tax to Indiana.  That is closed, over and done with, end of story.  You never get it back.

You should not pay NY sales tax when you register your car, if you are moving to NYS in 2023.  You claim an exemption using form DTF-803.   If you used form DTF-804 to claim a sales tax credit, that is the wrong form.  That form should only be used if you are living in NYS when you buy the car, but you buy the car out of state.  In that situation, the state where you buy the car and the state where you live will both charge sales or use tax, and form DTF-804 is used to claim a partial credit so you aren't double taxed.  

If you were living in NY when you bought the car in Indiana, you don't get any extra credit, as I explained in your other question.  If you were only living in Indiana when you bought the car, and you paid use tax when you moved to NY and registered the vehicle, you used the wrong sales tax form.  You should have paid no tax, and you would have to contact the DMV to see if they will let you correct the issue.