As the title implies, I've installed the expansion, and when I run the 1.0.2.1 update it says "Update already applied".
However, when I run the game, the menu says it's running 1.0.1.1.

Here's a screenshot of the menu.
I assume it should say 1.0.2.1?
Has anyone else has run into this?

It should.
Irrelevant, but i see ton of mules, By my experience it is easier to manage inventory with shared stash files.
They usually reside in C:\Users\****\Documents\My Games\Grim Dawn\save
transfer.gst for normal, transfer.gsh for hardcore.
Simply put, let's say, epic pants in shared stash, then copy this file into another directory named "epic pants", do so for every item type, and you will have nicely sorted inventory.
Can also be done during the game, even online, with single character, just don't open smuggler when you move files.