Whether the ship in "BoBW" was "in service" is debatable: for all we know, a museum piece was dragged back to service kicking and screaming for this single sortie (this stuff really happens in Star Trek, the most recently in Lower Decks).
Whether the ship in "BoBW" was a
Constitution is debatable, too. We saw bits and pieces, literally. But the
Miranda, the
Constellation and even the
Sydney are put together out of
Constitution pieces.
That said, there's nothing wrong with a
Constitution soldiering on in the 24th; starships tend to be like that, sometimes operating tens of thousands of years after their best-before date. And Starfleet is a veteran of maintaining logistics chains for a staggeringly broad range of designs, easily including some obsolete ones as well.
That said, the
Constitution appeared to be more a curse than an asset to Starfleet back in ST4:TVH already, with one awarded to Kirk in lieu of a gilded watch and then apparently only ever utilized for missions of humiliation, ones intended to fail. With the history of constant radical refits, no wonder: either there was something badly wrong with the design to begin with, or it was simply ages-old even back when Kirk first got the
Enterprise.
Not to divert too much from the conversation, but the bridge simulator in Star Trek II for the Kobayashi Maru is listed as being from the Enterprise-class starship. So it's possible as well that the refit in the movies was a whole new class of starship, and that to distinguish the two we can refer to the original series ship as Constitution-class and the movie ship as Enterprise-class.
And then it was back to
Constitution class in the paper graphic seen in ST6. Might be as simple (cough cough COUGH!) as real-world practices: there are different standards of construct and refit, and all are named after the first ship thus converted, even if the name from the first-ever ship of the first-ever version also commonly gets used overall. Only NCC-1701 was ever converted to the Motion Picture standard, hence the name for that subclass; but the
Enterprise-A was from a stock for which the refit was spearheaded by the
Constitution herself, hence
that name.
We don't know if other designs undergo such torturous refit histories, but it's quite possible. Curiously enough, we basically never hear what the class designation for a given starship design would be, not on screen; the ships we think are
Mirandas might have sixteen different class names "in reality" for all we know.
Timo Saloniemi