@jamill clued me into the solution in the comments above. Git has a slightly different workflow than what we are used to with TFVC. You must connect to the repository, not just the Team Project. I had to click the refresh button for the for repositories to show up, and then double click on the repository name to connect. After that, Work Items and Build show up as expected. Yay!
Before
Connect to the Git Repository in the Team Project
Tada!