No, there are no issues if you want to pay the taxes owed using the IRS payment website when e-filing your 2023 federal tax return using TurboTax.
Before you filed the 2023 tax return using TurboTax you were asked how you wanted to pay the federal taxes owed. You should have indicated mail a check and then e-filed your return.
Go to this IRS payment website and use Direct Pay, make sure you select Balance Due, Form 1040 and tax year 2023 - https://www.irs.gov/payments