That one photograph shows the entire job in a single frame: bare sanded mahogany on the left jamb, the first wet coat laying out across the baseblock at the bottom, and the difference between them. It’s also why we test before we commit. Once three coats are on an entire enclosure, you don’t get to change your mind about the sheen.
All three coats went on by brush.
Spraying a clear coat introduces problems you don’t want on a finish that hides nothing: entrapped air, bubbles, overspray, airborne contamination landing in a wet film. A brush gives the applicator direct control over how much material goes where, which matters on an assembly with this many rails, stiles, panels, mouldings, and transitions.
It’s also how marine and yacht varnish work has always been done. There’s a reason that tradition survived.