TMP and TWoK at least had rank insignia for non-coms as well as ensigns. TOS and NuTrek can't see the point. They think nobody will be paying attention to that sort of thing.
Noel was most likely a lieutenant. Science officers with doctorates tend to be lieutenants in TOS. More junior crew tend to be support staff like technicians, pilots, and admin staff.
Closest we've come to Chapel's rank is the old view that she was a Brevet (a provisional ensign a bit like Wesley) because she was not a full graduate of Starfleet and signed on the Enterprise in a hurry doing a job that was not actually her area of expertise. When she stayed on, at some point she became a full ensign and then a Lt in TAS. She was a Lt as a doctor in TMP and a full commander by STIV. My personal view is that she should have been allowed to become a biology expert rather than a second fiddle MD.