One possibility for the amount on your Form 1099-G being different than the amount carried over by TurboTax is that your state adjusted your refund after your return was filed. I would recommend updating the 1099-G in TurboTax to the correct amount.
Unless you itemized last year, your 2022 state refund will not affect your tax return this year. If you did itemize last year, all or a portion of your state refund may be taxable on your federal return. For more information, please see this TurboTax Help Article: Do I need to report the state or local refund I got last year? Is it taxable?