You can be pretty sure that TurboTax is correct.
When you do the manual calculation make sure you are using the correct calculation method. There are other things that affect the tax calculation besides the amount of taxable income and the filing status. There are seven different methods that can be used to calculate the tax on Form 1040 line 16, depending on what types of income you have and other things in your tax return. The IRS instructions for Form 1040 line 16 explain the conditions for determining which of the 7 methods to use, starting in the right column on page 33 of the 2024 Instructions for Form 1040.
If you are using the desktop TurboTax software you can see which method TurboTax used by looking at the 7 checkboxes in the Tax Smart Worksheet. You can see the Tax Smart Worksheet in forms mode. It's between lines 15 and 16 in the first section of the Form 1040 or Form 1040-SR Worksheet.