I see that the Academic Registry form enables you to change the official module leader. Can that form also be used to add additional teaching staff to a module (e.g., a TA/Tutor)?

The Academic Registry form is for module leader only. The official module leader (known as an ‘instructor’ in Brightspace) can add other teaching staff to the module, within Brightspace, using the “Instructors - manually added” role profile <instructions here>.