I have an update on our situation:
Working with support, and after a few rounds of calls, they determined a single user account that existed twice in our instance, one with a middle initial and one without, was causing our issue.
I’d like to fully explain since most of the comments evidently didn’t fully understand: We could not EDIT a lot of our profiles. This was NOT a scoping issue, this was NOT a browser issue. You would click “Edit”, using any browser, and you would get an infinite spinning wheel in the center of the pane. The only thing you could do after that is hit back or close the tab.
Support removed the bad user profile during a maintenance window from the backend, and we could immediately begin editing the profiles again.
My staff and I think it’s possible that a change on our side in Azure may have added the users middle initial to his display name may have caused this, but the actual reason is unknown.