Why is the gambling tax that I paid not added to my total income taxed paid?

The withholding from your gambling winnings is reported in box 4 of your Form W-2G. If you don’t see it on the TurboTax Total Income Taxes Paid screen, review your entries from your Form W2-G to ensure that you entered the withholding from each box 4.

Follow the steps below to review your entries:

1. Open or continue your return in TurboTax if you aren't already in it
2. Search for W2G (don't include any hyphens) and select the Jump to link in the search results
3. Answer Yes on the Did you win money or other prizes in 2022? screen and follow the instructions to review your W-2G.

For additional information, please review the TurboTax articles How do I enter a W-2G? and How to Use the W-2G Tax Form to Report Gambling Income.

and make sure what you see is not state income taxes.  the winnings could be below the threshold for federal withholding but be subject to state withholding.  if this is not your resident state you'll likely have to file a non-resident state return