You labeled the dilithium intermix chamber on the floor of the TOS Enterprise' engineering as a tank, that makes me wonder if you've ever watched the original Star Trek. The image below that is also mislabeled, the "pipes" behind the grid are power transfer conduits and so is the fancy looking conduit next to Kirk and Spock.
They're as much a tanks and pipes as the things in STXI and ID are.
Star Trek ran from 1966-1969, and at no point during that were the functions of anything in the engine room established. They were just bits of vaguely futuristic machinery. 1969's The Making of Star Trek
(co-author: Gene Roddenberry) puts engineering at the rear of the saucer section and speaks of self-contained energy generating warp nacelles. The 1975's Star Fleet Technical Manual
and USS Enterprise Booklet of General Plans
by Franz Joseph follow this, putting engineering on deck 7 - that thing in the centre of the room is labelled the "Impulse Syncrotron unit" and the pipes behind the mesh are the sides of the two massive impulse engines. It's only in more recent (1994-present) technical publications that have retroactively applied TNG-era technobabble to the TOS Enterprise. I believe the Star Trek Fact Files
in 1999 put engineering on deck 19 and call that thing the "matter/antimatter integrator"
So basically, you're quoting technobabble applied to TOS 25 years
after the series ended which gave those pipes and tanks new names and saying I never watched the show.
Your diagram has a purple area that's labeled as shuttlebay 2 when it fact that's where the aft torpedo launcher is. The shuttlebay lost a bunch of it's shuttle racks in favor of the platform that scotty protested the new torpedoes on and that platform also connects to the broadside retrofit torpedo launcher area. As seen in the movie.
My placement of shuttlebay 2 was a guess having only seen the movie twice.
Here's a blurry Youtube pic of the Into Darkness shuttlebay from a fanvid, showing that it's as big as ever (note the 40ft military transport shuttles from the prior movie lined up on the shelves, just as I pointed out from the outside!). I'll have to see the movie again to see if there's any direct connection between the shuttlebay and weapons bay.