Unfortunately most of the Star Trek games wound up as shooters were the diplomacy and philosophical segments were dropped.
Mobygames has a list of Star Trek games.
25th Anniversary and Judgment Rights nail the original series with OG cast doing voice over and really the best.
The FMV game Star Trek Borg is good for the sole reason it stars Q making fun of you the whole way through. There is another FMV game involving Klingons but its meh.
There are a lot of forgotten Star Trek 90's games like this Resident Evil knock off called
Hidden Evil which is a prequal to one of the last TNG movies, not a great game by any means. A FPS was made based on the generations movie, it is terrible.
One of the few Star Trek FPS games were it made sense was
Klingon Honour Guard.
A
Deep Space 9 game made in 2000 that was a decent 3rd person shooter.