If the EXTEST_33788774A21E4 user is not there and needs to be to run the test-outlookconnectivity you need to do the following:
open Exchange Management Shell and navigate to the Scripts directory
under where you installed Exchange, and run the
new-TestCasConnectivityUser.ps1 script to recreate the mailbox-enabled
user. It shouldn't matter that it creates a new mailbox; there
shouldn't be any data in it that is of any importance.
Again, I don't think this will fix Outlook Anywhere, but it will allow you to test it.