"Just a thought - if it were the bigger cargo containers as hinted at from TWOK, then I'd imagine that they were just flown out the shuttle bay. It is the largest hatch on the ship and we really don't know what is forward of the flight deck. It could just as well have a similar cargo structure as the TMP ship."
In WOK Chekov says "these look like cargo containers" and I remember from behind-the-scenes-shots (without obscuring sandstorm) that they used the TMP "standard" cargo containers. Someone rationalized they converted the exterior shell of the containers as roof covers for an underground habitat. Makes practical sense to me and you don't have to worry about the interior size of the habitat anymore.
If the square white hatch were not for unloading and lowering cargo containers to a planet's surface, we'd probably have to cram a specialized "Space Seed" cargo transporter into a section of the ship where there is already limited space because of the TOS corridors.