Yes, you filed resulting tax return is identical to one done by splitting the 1099-R, so there is no need to amend. The problem is that by not indicating to TurboTax that any amount was rolled over to a Roth IRA, TurboTax will not be tracking your basis in nontaxable Roth IRA conversions properly (line 60 of the IRA Information Worksheet). You'll need to correct your basis in 2022 conversion not taxable at conversion next year after you import your 2022 tax return to begin your 2023 tax return with TurboTax.
Splitting the Form 1099-R as I described allows correct tracking of your basis because TurboTax updates your basis correctly only if you indicate that the entire distribution reported on the entered 1099-R was converted to Roth. Doing so causes TurboTax to mark box B5 on it's 1099-R in forms mode. Years ago the TurboTax used to track the basis correctly whether you indicated that either all (box B5) or part (amount on line B6) of the distribution from a traditional 401(k) was rolled over to a Roth IRA, but the developers broke that functionality related to line B6 somehow and, rather than fix the actual bug they introduced, their "fix" was to simply not allow the reporting of only part of a code-G distribution as going to a Roth IRA.
