Statistics Update Time is missing in Actual execution plan
It is indeed in the execution plan, for those stats that were used.
There are two possible reasons why you don't see it:

You use an older version of the database engine, where this info wasn't present in the XML.

You use an older version of SSMS, which doesn't expose the info in the XML.


The answer to which of the above you have is by looking in the XML and see if the info is there. I'm on SQL Server 2019 and SSMS 18.5.
And you need to look at the right place, as well. You probably have to select the SELECT (outermost) operator, perhaps twice with something else in between, and view the Properties window: