403 is a category, not a code. Yes I know they're called http codes but REST calls are more complex than they were in 2001. There are hundreds of reasons you might not be authorized.
Is it insufficient permissions? Authentication required? Blocked by security? Too many users concurrently active?
I'd argue the minimum for modern services is:
403 category
Code for front end error displays
Message as default front end code interpretation
As json usually but if you're all using protobuf, go off King.