A few alternate interpretations:
The yellow warning color might be associated with antimatter ejection. We know from "Errand of Mercy" that there are antimatter bottles in or near Decks 10-11, and these could well be assumed to serve the photon torpedo system located in that area. The yellow hatch could be for ejection of this antimatter. The second use of the color, at the bottom of the engineering hull, would then naturally mark the ejection port for the antimatter used by the main power generation system. Circular doors are of course particularly difficult to open (where do you put the hinges?), lending support to the idea that this is a blowaway panel. The yellow dorsal rectangle aft of the bridge might warn about the antimatter stores of a putative aft torpedo launcher, or then of the dorsal forward torpedo launchers so eagerly suggested by Franz Joseph.
The trapezoids reappear on the Enterprise
-E primary hull underside, after having been absent for decades, in-universe and out-universe. We could see them as non-vital gear, rather than as vital gear that changes shape (and location?) for the intervening decades. The TNG and DS9 art departments make use of trapezoids mainly in various antennas. Perhaps these, too, are antennas for a specific system for sensing or emitting? By not associating the grey-with-grey-trimming shapes with hatches or openables of any sort, we would make life easier overall, as again the similarly colored T-shaped feature on the engineering hull would be awkward to hinge open.
Then again, the trapezoids appear to feature visible "hinges" at the stems, or at least have double lines there as opposed to single lines to the sides. And hinges would only be an issue with panels that need to open regularly to let large objects through; service access panels could be of any shape and open in more involved ways. But that tempts me to suggest that the almost invisibly grey-marked shapes would all be service hatches, very seldom accessed. Regular access would call for high-visibility markings.
Yet clear problems also exist with interpreting the red lines as denoting hatch edges. The putative hatches outlined in the nacelles can't open unless the nacelles are separated from the pylons; the lines in the saucer don't encircle any sort of a hatch. Perhaps red, another alert color, just indicates that a person or vehicle approaching is to stay clear of the marked area or direction? That is, the radiation flux from the nacelles might be particularly intense around the upper stems of the pylons, and the sensors of the saucer might have particularly strong radiation lobes towards the aft sectors marked by the red arches. Or the arches may denote the hazard posed by the nacelle ramscoop thingamabobs in line with the red markers - thingamabobs colored red themselves, in idle mode!
The main antimatter stores would get double warning colors: yellow area for "Evil may burst out at any moment - be prepared to dodge!" and red outline for "Even when you don't see it, Evil is pouring out from here - don't linger!".
we have never seen a TOS cargo transporter or a TOS cargo Bee.
Why would the ST:TMP hardware not qualify? It's only a decade removed from TOS at most. And it doesn't look or sound like the sort of hardware that would change much from decade to decade. Indeed, the very same Bees are still in use a century later.
As for "cargo transporter", we did see a unique transporter room being used for the sole purpose of transporting cargo in "Dagger of the Mind" - a room with a special exposed circuit panel at the back wall, perhaps reflecting the utilitarian-over-pleasant approach to transporting non-complaining loads. This transporter appeared to deliver its load to Deck 14 or below (as this is where we next see the stowaway who got aboard with the load), well matching the idea of cargo being stored on the lower decks.
(unless one seriously suggests a shuttle to take a nose-dive inside)
One certainly does. Why would a shuttle enter any facility crawling sideways or top or bottom first? A shuttle nose-dives into the aft facility, at any rate!
The off-white isn't exactly a high-visibility marking in this context, so it might ill serve as an approach aid for auxiliary craft. There aren't any associated guidance lights, either, unlike with the stern shuttlebay. This might significantly complicate something as "regular" as cargo loading.
The shape is quite acceptable for a hatch, though, and is located close to known or suspected auxiliary craft facilities. But perhaps it's just a case of the last starbase maintenance session involving the removal of this hatch, and its painting / replacement by another, of/by slightly different color grey?