Here is the honest map of what each role reaches. Two habits run through all of it: your client directory is shared across the whole business, while calendars and bookings belong to the branch they happen at.
The line worth noticing is the one between the desk and the timetable. Front desk staff run the day: they sign members up, take payments, book seats and mark who came. They don’t create the Tuesday 7am class or change what a plan costs.
Every staff role can read the working information of the business: the client directory, schedules, contracts and invoices at the locations they cover. Instructors are the read-only role, so they see their classes and who is booked into them without being able to change anything.
A grant at one branch stops at that branch. Someone scoped to Downtown sees the Downtown calendar, its bookings and its sessions; another branch’s day simply isn’t there. Clients are the deliberate exception: the directory is org-wide, so a member who usually trains downtown isn’t a stranger when they walk into your second location.
Editing the catalog and reading the audit log both need org-wide owner or admin authority, no matter how many branches someone manages. What you sell and who did what are decisions about the whole business; see Keep an audit trail.