I must say this Enterprise bridge really makes me wonder how Discovery fits within the Prime universe, since it looks like the Kelvin’s E’s bridge, where it’s as big as Voyager’s bridge 100 years in the future. In both “The Cage” and TOS, and even going upto TMP & STVI, the Captain’s chair is so close to the helm/nav chairs that Pike, Kirk, Saavik & Sulu are nearly scrapping their knees on the helm/nav chairs (in STVI, we can tell that the Excelsior has more room between the Captain’s chair and the helm/nav chairs as Sulu has a table for his tea in between and doesn’t look cramped behind the table, but that’s another class) whereas in Discovery it appears that there is as much space as Janeway has between her chair and Paris’ chair on Voyager. Plus in TOS, the upper ring seems to be just big enough for someone to pull out a chair and sit, while someone can walk by, but Discovery’s look like 3 people could walk behind a seated person.
But even if the Discovery E has a different module than the Cage E and TOS E, it doesn’t make sense how it could fit, as the bones of the ship could only support a certain size of module. It’s like now if you buy a single story house and you wanted to add space in the attic for say a bedroom, most people add dormers which don’t need as much structural work as adding a whole new story that would require making sure that the lower part could hold up the new second story. So Discovery’s E doesn’t seem to fit, especially when years later, Starfleet couldn’t add a bigger bridge during the Enterprise’s 18-month refit.