Picard would have still known it was a Constitution-class bridge--regardless of it being original or refit--by both the ship display near the turbolift and, of course, by Scotty being there.
Quite probably so. But if Picard considered any arbitrary bridge layout "Constitution
class", the scene would lose much of its meaning. And so far, visual proof still supports (or allows for) the view that TOS era bridges might have been class-distinct and thus the holo-simulation could have been specific to Constitution
, whereas TOS movie era and later bridges have a great variety of arbitrary layouts that tell nothing about class identity.
Or, it was the last of the Constitution-class ships to be retired from active duty and was placed in the Museum after Scotty's disappearance.
I find it difficult to believe that Starfleet would keep any TOS configuration ships in active duty in the 2290s, two decades after the first verified refit of one. This was a time of heightened tensions with the Klingons, so the UFP would be pouring resources into Starfleet - and every ship we saw in the movies (regardless of class) was of the "refit era", without remaining TOS aesthetics to either the exterior or the interior.