Am I supposed to put state tax refund received from 2023 It states "Add up any payments you made to your state from the previous tax year Amounts withheld on your W-2"?

No, you do not want to enter the state tax refund you received, but rather any state tax payments you made, including:

 - Amounts withheld on your W-2, W-2G, and 1099

 - Estimated tax payments 

  - Add any paid this year for last year (it's common for the fourth quarterly payment to be made in January)

 - Overpayment from prior year applied toward your current year return

 - Payments made with an extension of time to file

 - Payments made when you filed your return

 - Refundable credits

Amounts withheld for your state during 2023, and showing on:

1) 2023 W-2 forms

2) any 2023 1099-R forms

3) any other 2023-related1099-??? Forms, If any (though that's not common).

4) any State quarterly estimated tax payments you might have made during 1Jan -to-31 Dec of 2023.

5) If you owed extra for 2022 state taxes, and paid them when you filed 2022 taxes in 2023...include that.

But they only make a difference if you used Itemized deductions on your Federal 2023 tax return.   IF you used the Std Deduction, then there is another follow-up question you will get to that asks you which you used on your 2023 tax return....then, if that was the case, when you select that you used the Std Deduction on your 2023 Federal tax return, the 2023 State refund is then not included as income for 2024.