My question is -- When they re-use music from other movies/shows, is that the composer's choice? Or is that the choice of the music editor? Or even the producers/director? Not that it really matters, but I'm just curious.
All of the named individuals work together in "spotting" the music, i.e. deciding what goes where, but as with everything else, the final decision lies with the executive producer. Normally, per modern union rules, every episode needs a full original score, so even if themes or cues are reused, they have to be re-performed. Judging from the liner notes to the Ron Jones TNG set, the only times a pre-existing cue was tracked into an episode were when the executive producer rejected the cue the composer had written for a scene and they had to substitute something else.
As I recall, the "Way of the Warrior" music was not absolutely verbatim the same music from Generations
, just a very close restatement. I'd assume that was the case here as well. So it would've been a new recording, not a tracked cue. If it were tracked, it certainly wouldn't be listed in the CD credits as a separate piece. It would be credited under its original name, catalog number, and other specifics.