The W-2c is correct. The repayment in 2022 does not change the wages reported on your 2021 tax returns, and does not change your 2021 refunds. If the amount that you repaid is $3,000 or less, under current tax law, for years 2018 through 2025, you get no tax adjustment for the repayment. If you repaid more than $3,000 you report the repayment on your tax return for the year that you repaid it. So you will handle the repayment on your 2022 tax return.
The federal and state taxes that were withheld in 2021 were paid to the IRS and the state, and were applied towards your 2021 tax. It doesn't matter if less would have been withheld if you had not gotten the bonus. Your 2021 tax returns reflect the amounts that were actually withheld, even if it could have been less under different circumstances.
(You don't really want the withheld tax to be adjusted. Doing so would mean that you would have to pay more tax to make up for the reduced withholding.)
