We moved to SC from NH in 2023. TurboTax is prompting me to enter information for a SC underpayment penalty for 2022 but we did not live here. It’s costing me $59. Why?

If you owe more than $100 for the time you lived in SC, then you would be subject to an underpayment penalty.  The question is generally what was your tax liability for 2022. TurboTax is trying to fill out form SC 2210 to see if your penalty for underpayment can be waived.  If you did not live in SC last year, then the answers for all of your questions regarding your income will be $0.

I'm not specifically familiar with the SC software, but the general rule is you can forego calculating the underpayment penalty and just wait for SC to bill you, which they may not do, since it's your first year.