Cite related work from same year as defense?

Of course, you should include anything that is relevant regardless of when you started your thesis.

I have even seen dissertations that cite work that is unpublished or still under review.

If the section is called "Related work", it should include work that is related, regardless of when it was published. If the section is called "Related work that was published before I even started my PhD", then it only needs to include work that is related and which was published before you started your PhD.