@asharpe You need to click on the DBMS. The plugins show at the DBMS level, not at the DB level. I downloaded my Desktop version a few days ago. See below -
At the DB level, I see no plugin options either -
See how in both pictures it says Active DBMS - Graph DBMS. Yours says 'No active DBMS'. Try re-downloading Neo4j Desktop. It should come with the example project with Graph DBMS.