Add up any payments you made to your state or locality, along with any state or locality withholdings from the previous tax year,

No, it is only asking about withholding for the year the state tax refund was from. If you filed on time, that would be 2022. 

I assume you are trying to complete the section about your 2022 state tax refund that you received in 2023. If that is the case, you are being asked for the amount of state taxes paid for your 2022 tax return.

Here are the box instructions with clarifying notes in bold:

"Add up any payments you made to your state or locality, along with any state or locality withholdings from the previous tax year, including:

- Amounts withheld on your W-2, W-2G, and 1099 - 2022 forms only
- Estimated tax payments for 2022 (including any paid in 2023 for 2022 - it's common for the fourth quarterly payment to be made in January)
- Overpayment from 2021 applied toward your 2022 return
- Payments made with an extension of time to file - for 2022 only
- Refundable credits - for 2022 only"

Yes, the amount of state and local income tax withheld is the amounts from boxes 17 and 19 of your W-2.