I believe that Schedule H is required even though estimated payments were made by my payroll company. But you are right that the calculation of taxes due will be overstated by TurboTax if one fails to include the amount of estimated payments made towards 2021.
Lastly, I did confirm that you should include the amount of federal withholdings on the Schedule H. When I did that, the amount owed matched exactly the amount on the Schedule H prepared by my payroll company.
