Where do I report my anticipated MN state taxes paid on the tax return?

You actually enter these in the federal portion of TurboTax.  

To enter your state estimated tax payments  in TurboTax Online:

1. Open TurboTax Online
2. Select Tax Home in the left pane
3. On the Hi, let's keep working on your taxes! screen, select the dropdown on the right side of the Deductions & Credits box, then select Start, Continue, or Pick up where you left off
4. Scroll down and select the dropdown to the right of Estimates and Other Taxes Paid
5. Select Start or Revisit to the right of Estimated Tax Payments
6. Select Start to the right of State estimated taxes for 2023
7. Select Yes on the Did you pay state estimated taxes for 2023? screen
8. On the How much did you pay in state estimated taxes? page, you can enter the amount paid.  Note that you can change the date paid from what's populated on the page.  Once done, select Continue