This is a tricky situation, and might be a little hard to understand. But everything's okay. The amount of your 2020 overpayment that you applied to your 2021 estimated tax is not really a carryover. The amendment to your 2020 tax return will not actually affect your 2021 tax return.
The full amount that you applied to your 2021 estimated tax will remain applied to 2021, and your 2021 tax return should show the full amount that you originally applied. You will have to pay back the difference as an amount owed on your 2020 amended return. The amount you will have to pay with the amended return will be the difference between the overpayment shown on your original 2020 tax return and how much the overpayment would have been if you had not overstated the business expense. The amended return takes into account the overpayment on the original return. It does not take into account the amount that was applied to the following year.
So the answer to your original question remains the same. You do not have to file the 2020 amended return before you file your 2021 tax return. Some time after your amended return has been processed, you might get a bill from the IRS for interest on the amount you had to pay back.
