No, you don't need to file the 2021 amened return before e-filing 2023. It will not affect your 2023 return because you contributed and converted the funds in 2021, unless the converted amount was less then the contributed amount, then you would have a basis on line 14 of the 2021 Form 8606 to carry over to 2023.
Please see How do I amend my federal tax return for a prior year?
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