After entering the estimated taxes we paid this year for a household employee (nanny), our tax bill went up significantly in-app. I'd like to understand why this is.

Put your total federal withholding in the box shown below.

Continue through your State Unemployment section till you get to the screen that says Total Household Employment Taxes.  That number should equal the amount of household taxes you're liable for.

Then, go to Estimates Paid:

1.  Click Federal on the left-hand side menu.

2.  Click Income & Expenses across the top.

3.  Scroll down to Other Business Situations and click Show more.

4.  Click Start or Revisit by Estimated Tax Payments.

Make sure your estimates are correct.  Basically what you're doing is putting the taxes on (entering wages paid to your household employee), then taking them off (paying estimates).