I had a support ticket that has been resolved (115267). In the resolution, it was recommended that I request the change here.
Here is the reply for reference:
"I have worked through the code used by the Snap personal menu to display deadlines and forum posts. Unfortunately, neither feature takes role directly into account. If the user has the capability to read the forum, then new posts to the forum will be included in the Snap menu. Likewise, if a deadline event is visible on the user's calendar, the event will be included in the deadlines section of the Snap menu.
I understand the use case you are trying to achieve and can see where it would be valuable for the Snap menu to focus on the courses the user is teaching and not be cluttered with events for courses they are merely observing. I would encourage you to engage with us on this feature need in the Open LMS Community"