> The guy wears a suit, tie and hat to the session!
TO, but not during, the session. Gotta look neat on the street. Recording was work, jacket and tie would come off. BUT that color photo is clearly a Photo Shoot, not a Recording Session. Look at the light! It is smack in the musicians' eyes. Also it looks like ISO64 film, yet not a time-exposure: it was BRIGHT in that room. There is a honking big light to the left, a lesser light to the right. Optimized for Sinatra's face but also washing the band. I bet the band could not read their scores for 10 minutes after they turned those photo lights out.
The B&W photo is harder to read. It is in candid style, but has been set-up, but maybe set-up in a very general way. It has the look of Tri-X (or over-developed Plus-X) in a Rolli, handheld. Maybe the photographer set up lights at rehearsal and then snapped 100+ pictures over an hour, until people forgot he was there. Or maybe the idea was to pose Sinatra in the puddle of light at the left for a Posed Photo on the color-camera, like the one above; but before or after that formal shot the photog saw this scene and grabbed it with the Tri-X Rolli/Leica we all carried for candid work.
> They're tracking everything live!
Of course. Sinatra was a live act. He had to hear the band. The band had to follow him. His recording work evolved, but at the time of these pix he was doing what he did in the dives of Hoboken, just more slow and careful with re-takes.
> The room is so big you can't even see the back wall or the ceiling in the shot!
The ceiling is visible... about 18 feet. That's actually a small room for big band. You don't want to be that close to horns. Our 15 foot hall is painful with just one trumpet.