I think the second Akira you are looking on the lower ring is actually a Yeager class. I would have guessed USS Thunderchild was the Akira in the museum, but she did appear in Season 2.
I know I'm late to the party about this and I haven't seen the episode yet but I've seen the clip with Jack and Seven talking about the ships and if anyone is still bothered about the USS New Jersey not looking like the Disc/SNW Enterprise, Jack clearly refers to the Ent-A as Constitution class, he doesn't mention what class the New Jersey is. Maybe when they originally filmed the voyages of Kirks ship the producers couldn't get Starfleet to lend them a Constitution class ship to play the Enterprise so they just used a knackered old New Jersey class ship assuming the audience couldn't tell the difference. When they came to film Pikes era they were granted the resources to make it look right. Hence the ship is a proper pre-refit Constitution and the bridge doesn't look made out of cardboard and duct tape. There. I've solved it for you.
None, would be my guess. Just a nice Easter egg. We saw the Cage Connie in DISCO through archival footage. It made no difference in DISCO or SNW.
Seeing that NX Refit in the distance was a very, very heartwarming moment. It's been a long road getting from there to...there.
It's kind of nice simply knowing these ships weren't destroyed either by battle/accident or retirement.
I guess this means that this is what the NX-01 looked like at the time of the ENT series finale set in 2161? We never actually did see the outside of the NX-01 in the final episode except for the flyby of the three Enterprises as the "Space, the Final Frontier" speeches are read, and with the exception of the episode-specific 1701-D those flybys could be generic beauty passes.