On the DropShip. Those things carry quarters for a reason.
But probably not for a long deployment. Then its going to be getting uncomfortable and if a Warships thrusting around then you're having to launch the dropships every time she lights her main engines, burning their fuel to keep up.
The way I see Dropship CV's is as the WW2 equivalent of a CVE, yes they can carry fighters, but they don't have the capacity to support them for long in the field due to lack of carrying space for spares etc. Using my Titan example, she carries just over 2000 tons of cargo (2085 to be precise) and if you're berthing your crew aboard then thats going to be food, water, consumables + ammo for fighters + any spare fighters etc, it don't leave much. So on a longer mission that's not *jump* PUNCH SOMEONE IN THE THROAT *go home* but say a multi-month patrol, you're going to have to draw off the ship you're attached to. Dropships have been described as being uncomfortable and with iffy air recycling and a unique smell to them in the books, and even at the height of the SLDF you're probably going to run into habitability problems if you keep the crews onboard these small, short ranged vessels for a long period of time.
Also where are the support vessels? We know that space mines are a thing, so there should be a mine hunter/sweeper ship that can dismantle a field or act as a base for small craft that can do so. Yes we know the Newgrange was a thing, but you'd not be able to deploy those everywhere, so where's the smaller repair/supply vessels to support you on missions far from your support structure and bases. The Newgrange is a strategic asset, not something you break out for every deployment.
Yes I know i'm thinking blue water navy, but the SLDF's fleet structure, its support infrastructure makes little sense. And its more top heavy in combat units and lacking in support units than the US navy was pre-WW1.
By which I mean that Pre WW1 the USN had a big fleet of battleships and armoured cruisers, but if you went to them
"Okay what about escorts and scouts?"
"Deeh-stroy-urs?" *blank faces all round*
The fleet had literally no modern destroyers, even for the period, and it wasn't until the huge emergency building programs of 1917 that the USN went "Oh yeah...we'd actually better screen our ships....doi-hoi-hoi." Whilst this was just the result of budgetary stuff (you could fund a BB easier than a DD) it was a huge problem. And this is kind of whats happened here. The SLDF has like ALL the warships EVER. But nothing to actually support them in canon outside of the Newgrange. And yes you can use dropships, so what carries them, more warships? Jumpships waiting behind the line, all alone and vulnerable? Why not have a logistics transport, its whole life dedicated to carrying fuel, ammo, spare parts, crated fighters etc. DropShips dock, take what they need and go to their ship in need. But no, there's next to no logistic support for the SLDF once it operates outside of the hegemony.