It's no big deal. I'm also fine with the idea that more were built. It was a successful ship. Why not build more? It just seems like when picking one to include in this episode filled with Easter Eggs, why not use one that would mean something to TOS fans? Not a huge deal. But oh so simple to do.
Looked it up. In the original series proposal, the ship was going to be named the Yorktown. That would've been a cool reference. First Draft Star Trek Proposal
It's not clear what point you're trying to make here. Having a TOS Connie is for TOS fans. Who else would it be for? I'm just saying it would've been a nice thing to do for TOS fans. And simple too. Just give it a different name but literally everything else could've been the same. That's not making it all "about TOS fans."
TNG fans, and specific episode call backs. Well, this escalated quickly..I said nothing like this. I was actually disappointed at the name. I would prefer TOS get some love. It won't though.
They may rotate the ships in the outer docking rings and the rest are inside the superstructure, parked like active duty starships inside the Earth Spacedock. The 1701-E could well be inside the Museum.
Like I said, it wasn't clear what point you were trying to make. So, I guess I misunderstood. Sorry. But I still say that the TOS Connie was there for TOS fans. Seems obvious.
The Fleet Museum is like Petersen Automotive Museum in LA and I'm sure like all museums. They have stuff on display but also stuff in vaults. And they rotate things in and out. I mention Petersen Museum because now you can take their vault tours to see the stuff not currently on display. (And it's pretty damn awesome!) I wonder if the Fleet Museum has a vault tour?!
It was a K'T'Inga, it looked like it had Kronos One's paint scheme, so probably Kronos One. The end credits mentioned a USS Pioneer at the museum, but wasn't seen. So it might have been inside.
Given all the ships in Prodigy had duplicate names, unless it's explicitly confirmed, I'm not going to assume the real Defiant, Centaur, Thunderchild or (sigh) front-half-Sovereign/back-half-Enterprise were among the ships that were there. That bit (from Michael Jan Friedman's "Crossover") has the same issue that the Yorktown-is-Enterpise-A theory does, that we see the Yorktown in the movie. Well, the bridge. And the novel did mention that the Enterprise's pre-refit bridge was fitted to the ship for the exhibit, I can't remember why the Yorktown's wasn't usable, so I suppose it's possible the ship was unrefitted on the outside but was upgraded with movie-era styling on the inside. Brian Tatosky said on Mastodon that the Akira on the lower level was standing in for the Pioneer, which was having work done on it that day and was inside.