As I wrote previously, what happened in 2021 stays in 2021; same for 2022. Thus, assuming the HIT amount withheld in 2021 was accurately determined based upon your 2021 income, you have not basis for requesting a refund. My comment about remembering the FICA withholding was intended to:
1) Remind you of the fact that FICA was withheld, and
2) Allow you to use this info in your negotiation with your employer on how to proceed in your repayment of the overpayment.
Lastly, the idea behind reducing your hourly rate for a time in 2022 is that between your 2021 actual payments and 2022 payments, everyone breaks even. (Everyone includes you, your employer, and all taxes paid.)
If you can negotiate a better deal for yourself you may make a bit more than if your employer had not made the error.
Good luck.
