All the Enterprise ones are on the same deck as the shuttlebay floor, save for the bowmost which is one deck up. Decks 16-17, then, assuming (as the window rows would suggest) that scaling doesn't affect deck count in the TOS vs. DSC analysis. Which really is TMP vs. DSC in the end, as only that movie bothered to be specific about the decks. Then again, the DSC bridge is on what in TOS would be Deck 2...
The Discovery ones are two and three decks up from the thick stem of the neck, or one and two decks down from the saucer bottom, FWIW. Make of that what you wish. But since there are no hints of these tubes before they emerge, on either ship, we may postulate there are tubes on every deck and these four were activated here but others might be chosen in other docking scenarios.
How many of those shuttles would be Enterprise ones, one wonders...? There was that opening shot and then the scene with the inverted camera and the workbee where it appeared as if the Discovery were the actual processing center getting these shuttles (and landing pods) combat-ready, perhaps also processing NCC-1701 ones. In contrast, the Enterprise only ever disgorged those compact "combat fliers" on screen.
Did they even bother to create a shuttle texture that would have ENT or 1701 on it? The only shuttles we see up close are Po's and Spock's, both DSC craft. (#12 and #23, respectively, but Kirk had #7 in TOS despite there never seeming to be more than two shuttles available at a time.)
I still want to market the idea that the Discovery is a repurposed shuttlecarrier hull, her secondary hull now crammed full of labs and mushroomrooms and whatnot, but her thick neck also having originally housed a big hangar (with an apparent immense square hatch on the leading edge, above the one and only row of portholes) and is now host to nothing but creatively rerouted turbolifts and impromptu logistics space. The saucer may have permanent corridors and decks and rooms in between; the rest of the ship has modules bolted together, rattling inside a big hollow cavity. Maximum flexibility for wartime experimenters in-universe; maximum flexibility for writers and VFX artists out-universe.
Timo Saloniemi