I'm guessing there were other clusters of shuttles ahead of those. Winona's was Medical Shuttle 47 so there were clearly more than 20. And even if there weren't, could each of those shuttles hold 50 people? They are bigger than any of the TV Trek shuttles.
It would be a tad odd for any of the shuttles to be outside that main gaggle. We see a steady stream pour out; we see young Jimmy's shuttle among the last to leave, and that one is supposedly included in the gaggle. But yeah, there might be two gaggles, for whatever reason. Or outriders, or whatnot.
OTOH, where would more than 20 shuttles have been stacked inside the ship? We see the three-tier shelf structure, and the depth of the bay, which doesn't really allow for much more than this. And I really doubt the ship was supposed to have 46 medical shuttles in addition to the one we saw... (Kirk never could spare seven shuttles, either, even when one or several of them carried the number 7. Or a dozen, when one or several of them carried the number 12 in TAS.)
As for shuttle size, these are fairly small craft, no bigger than the ST5:TFF prop. And we can see those 20 are all the same model (even if one is colored red and white). A runabout about thrice the size could carry sixty in "The Homecoming"; a largish lifepod built out of runabout set pieces only held about a dozen in "Emissary". I gather packing 'em ultra tight would be an option, but apparently Starfleet doesn't do that in evacuations, as per "Emissary".
I'm betting the Crossfield class are glorified R&D / Experimental Technology Field Testing / Secret Technology Data gathering vessels.
And possibly recycled former frontline ships at that. The USN found many uses for retired flattops; Starfleet might have built these ships with their extra wide shuttlebay doors and oddly shaped secondary hulls as carriers originally, too (as fandom has long insisted), and then used all that internal volume for other applications much like the USN used all that free deck area.
The reason the ship is designed the way it is, is simplicity / speed of construction.
Or then Starfleet just polishes the shuttlebay floor after having converted half the hangars to mushroom conservatories and otherwise refitted the awkwardly shaped ship to its new use.
Obviously the Discovery & Glenn's spinning hull should be a pair of one-off variants from the original Crossfield Class designs.
Or two out of the three or more that were converted from the original carrier to the modified flying lab, starting with
USS Crossfield of that so far unnamed original class. Examples of the original class might still be around, too - but
Crossfield would indeed be a brand new (sub)class, without any of the keels actually being new.
The original Crossfield should have standard Starfleet Saucer sections.
Hard to tell. The surprisingly knowledgeable convicts in "Context is for Kings" did not indicate they recognized the exact ship design, but they did not comment on the split saucer being exotic, either. Perhaps the spinners have other uses besides bleeding off <whatever> during spore jumps?
But overall, they are designed to be out in Deep Space to test stuff, and defend the secrets of the experimental technology & research as necessary.
Rather poorly at that - even phasers on double hot (with impulse drive crippled by this mode) didn't seem to do much good against the smallest known Klingon warship type. Then again, the ship seems to have lots and lots of torpedo tubes (none exactly visible) as per the sight of them pouring out towards the Ship of the Dead.
You look at the "Constitution Class" and it looks far more "Advanced" in design compared to a "Crossfield Class".
Well, it does have a higher registry number.
Timo Saloniemi