The taxes withheld in 2020 are reported in box 4 of your form 1099-G and are entered on your 2020 tax return and you will get the full credit of the taxes withheld in 2020.
When you repay the overpayment, you'll have to repay the gross amount (in your example $2,000). You can only claim this repayment only in the year you actually repay the amount.
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