Looks like the one I need. Unless it's not updated in any other scenarios.

pxAssignDateTime should be the one. 

You can run the use case and collect the tracer log. You can restrict the trace just to the Pega-ProCom ruleset if you want.  From the tracer, you can easily trace for pxAssignDateTime, and you'll see the value upon entry and upon exit of each activity.

I saw an old case with similar issue - The pxAssignedDateTime property for the workbasket and worklist record doesn't seem to have the value of when the object was assigned to the workbasket. It seems to have the createDateTime value though. The solution for this was that customer deleted and recreated the rule from scratch and the issue went away.