The ship rising from the water is the Enterprise which had been hiding while on a mission on another planet this was revealed long ago.
Now i'd say there's reasonable doubt that it may not be Enterprise as the warp nacelles appear less bulky although that could be due to atmospheric burn off. Upon closer review I noticed that even the pitch of the arms that support them appear further apart plus the deflector portion seems to be almost compressed. Going by the footage it's hard to determine if Harrison is controlling another Starship could he possible have stolen an older model somehow? He certainly seemed to have a lot of followers so it wouldn't be a stretch by any means and given his occupation it's possible he already had special access. If the segments are completely unrelated then I would go as far to say that first part we see is from Kirk having a nightmare cuz afterall we all know it's his ship and crew.