Okay...so what happened to Constitution herself?
Funny story. Short version (long version possibly included in later chapters) is this: It's common practice for Starfleet to build a "ground test article," basically a full-sized working prototype of a starship class for testing system integration, computers, upgrades, and so on. The test article is effectively a completed and fully operational starship with no warp drive or deflectors installed.
The original test article was NX-1700 and was supposed to be named Enterprise while the first operational ship was to be the Constitution (so it actually should have been the Enterprise
class). Admiral Marcus didn't like the idea of the Enterprise name going to what was essentially a dummy starship, so he had them switched, justifying it by claiming he wanted to name the entire series after famous aircraft carriers.
King Daniel Into Darkness wrote:
I like the comparison between the "design proposal" and finished vessel. I'd previously figured that the TOS Constitution design never existed in the alternate universe (i.e. what we got was this timeline's plan A, based on different design parameters a the project's outset), but after seeing that NCC-0718 hologram in the ID deleted scene and read "old style Constitution-class" somewhere (either one of the Starfleet Academy
novels or a fanfic) I've wondered how both designs might have co-existed somehow.
As for the USS Vengeance, the novel The Return
featured a Defiant-class ship with a similar paint job, described as a layer of "microdiffracted carbon" to absorb visible radiation.
I liked that novel. IIRC, it also featured a type of Starfleet battle gear that included personal forcefields and some kind of powered armor