If the only state tax payment that you omitted was made in 2022, it will not affect your 2021 federal tax return, so there is no reason to file an amended federal tax return.
When you file your 2022 tax return, if you use itemized deductions on your 2022 federal tax return you should enter the state tax payment that you made in 2022 so it will be included in your itemized deduction for state and local taxes. If your itemized deductions will not be more than your standard deduction, the state tax payment will not affect your 2022 federal tax return.
Since the payment was for 2021 state tax, it will not affect your 2022 state tax return.
