Nope, brand new, never used before design.
Sorry, I had my logic reversed. TFF made it first, the it was cannibalized for TNG to make the Type 6.
I just assumed that since the budget for TFF was so small that they reused as much as possible from TNG.
It was 78 years later, though, so I would expect technological progression,
That was part of the problem with TNG in general. Why move it 78 years ahead? So that the TOS actors would not be included other than the cameo by an elderly McCoy in the pilot for the hand-off. Of course, they wound up having Spock and Scotty and Sarek show up anyway.
The era that TOS and the movies were in were ideal. When they moved it ahead they shifted the timeline to a much less interesting period in Federation history where there was less exploration left for them to do. TOS felt like a frontier and TNG felt like endless diplomatic missions with the Borg and Q being the main things to liven it up.