I contributed a non-deductible $6,000 in the tax year of 2022 to an IRA. I submitted my tax forms before I performed a Roth conversion. Do I need to amend my tax forms?

As you did the Roth conversion in 2023, you will report it when you get the form 1099-R for tax year 2023 (in early 2024).

You do not need to amend your 2022 tax return.

Please read this TurboTax Help article for more information.