Yes, what you propose is OK. The Roth contribution does not affect your Roth conversion and your Roth conversion does not affect your Roth contribution. Assuming that you perform the Roth conversion in 2022 (it seems that you might have already done so), in 2022 TurboTax you'll enter the $1,500 traditional IRA contribution, the $4,500 Roth IRA contribution. For the Roth conversion you'll enter the code-2 2022 Form 1099-R that reports the distribution from the traditional IRA and indicate that you converted all of this distribution to Roth. The conversion and the Roth IRA contribution can go to the same Roth IRA or to different IRAs, the taxable result is the same.
