How are bags transported from the terminal to the airplane?
From your photo this answer assumes a hub airport.
Some background first: after check-in, the belt conveyor system moves each bag onto its own tray – that's the modern individual carrier system (ICS) which mitigates jams, misreads, and lost baggage. Depending on how early the check-in took place, the tray will either go to a holding area, or directly to the baggage makeup area/space (BMA) where the bags are unloaded onto another belt conveyor system for cart/ULD loading.
BMA is the place you referred to as sort area. There is typically one BMA per airline per pier, and since big airlines usually have their own piers, it's one BMA per pier. Example for San Francisco Intl (see tan colored areas):


— https://www.flysfo.com/about-sfo/sfo-tomorrow/passenger-terminal

Two hours or so before the flight's STD (scheduled time of departure), comes the cart/ULD staging. The cart train length varies; IATA recommends 3 carts per narrow-body and 5–6 per wide-body. Airlines however implement this as best fits them. Easyjet for example stages one cart per narrow-body at Liverpool (internationalairportreview.com).
Regarding how many gates are served per BMA, one of the methods used to estimate the floor area required for a BMA when designing an airport is the EQA, or Equivalent Aircraft factor (see FAA AC No: 150/5360-13 for more).
In short, it's option 2.