Hi there, @afwright.
The Class Tracking feature only allows you to assign classes into income and expense accounts. Thus, assigning to assets and liabilities accounts isn't available.
Here's how you can assign classes to income or expense accounts:
- Go to the List menu, then select Chart of Accounts.
- In the Account drop-down, click New.
- Select the income or expense account type, then click Continue.
- Enter the information and choose the Class from the drop-down.
- Click Save & Close.

I'm adding this article for more details: Set up and use class tracking in QuickBooks Desktop.
Just in case you want to run reports by class, feel free to check out this article for more guidance: Filter, sort, or total reports by Class.
Keep in touch if you need any more assistance with this, or there's something else I can do for you. I've got your back. Have a good day and stay safe.