Hereís a bit of a drill-down on the shuttlecraft we saw
Galileo (the first one)
Galileo (the second one)
Da Vinci (from Starbase 4)
Picasso (from Starbase 11)
Also, we did finally see Cyrano Jones' ship, the Spacematic.
Lastly, it occurs to me that we also see the U.S.S. Intrepid.
I assume the shuttle names there are mostly from Remastered? In my list I've separated remastered versions where they differ from the original.
What the heck is NCC-K7?
Also, did we actually see the Spacematic? I don't it actually being visible other than maybe as an indistinct light colored spot in the hangar bay in the remastered (maybe) and DS9.