I just looked also and I think you cannot add a competency to a manually graded item you have added to the gradebook.
I think you can work around the limitation by creating an assignment and remove all the checkmarks for submission types. Set Activity completion to Show activity as complete when conditions are met, with a condition of, Student must receive a grade to complete this activity.
Being an assignment, you can then of course, add a competency to it. The assignment will show in the gradebook, you will have to add grades manually just as you would for a manual item, and the assignment will include competencies you used during setup.