Schedule H

Yes, you do.

Schedule H is typically filed with your individual tax return, although it can be filed as a standalone form if you're not required to file a return. 

According to How do I file Schedule H? in the Instructions for Schedule H:

File Schedule H with your Form 1040, 1040-SR, 1040-NR, 1040-SS, or 1041. If you’re not filing a 2022 tax return, file Schedule H by itself.

It appears that Care.com will prepare Schedule H for certain clients, but they don't file it for you.  You'll need to file it with your return.

To enter the relevant information in TurboTax Online:

1. If you don’t see 2022 TAXES in the left pane, scroll down and select the dropdown to the right of Other Tax Situations and select Let’s get started, Pick up where you left off, or Review/Edit. 
   • Otherwise, in the left pane, select the dropdown to the right of Federal, then select Other Tax Situations 
2. On the  Your uncommon tax situations page, scroll down and select the Show more dropdown to the right of Additional Tax Payments
3. Select  Start or Revisit to the right of Nanny and Household Employee Tax
4. Answer  Yes on the Did You Have a Nanny or Household Employee? page 
5. Enter any relevant information on the subsequent screens

Hopefully this will save some people some time.  I just got off the phone with TT. They said I have to snail mail file it.  Very disappointed that TT did not think to resolve this in 2021.  This nanny tax thing was because of the whole pandemic and I figured that after the first year, they'd have done something about this.