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"If they reduced your box 3 and 5 wages by the amount of the $5000 repayment, then boxes 4 and 6 should be reduced by $310 and $72.50, and so they owe you a check for $382.50."

You're spot-on about the adjustments on boxes 4 and 6. I'll reach back out to them about a refund for the SS/Medicare overpayment.
Regarding form 843, that would be attached to 2020 taxes since that's what the W-2c was amending? I know the Claim of Right process is next year, so I just want to confirm I understand correctly.