The taxes withheld on the 2020 Form 1099-R you received were what Fidelity withheld based on their requirements for withholding taxes on a distribution and amount was reported as tax payment on your 2020 tax returns. It had nothing to do with the 10% early withdrawal penalty. The penalty, which was not assessed since this was a Covid related withdrawal, would only be assessed on your federal tax return, nowhere else.
You have been reporting your 1/3 of the withdrawal correctly. It is 1/3 of the gross distribution from box 1 of the 2020 Form 1099-R. Not 1/3 of the amount you received after taxes in 2020.
