After a second listen, and taking into account the song's melody and not just the chords, I think what the song is doing in the first part is this:
- on Bm : the song wants you to think the Bm is iv of F# minor
- on Gm : the song wants you to reconsider and think that maybe the Bm was actually a i chord, and now it switched from D major / B minor to D minor, and Gm is iv of D minor.
- on F#m : the song says "gotcha", F# was the actual tonic after all
In my opinion, each of these momentary interpretations is equally correct at that specific point in the song. The perceived tonality is changed all the time, and it's in some way the whole point to make you re-think the harmony all the time. It's like the effect of a modulation in a pop song, but you get that sensation all the time. Like polyrhythms do for the feeling of meter and pulse - there are multiple equally "correct" interpretations going on. Although for harmony modulations, it's more like a wave, moving from place to place. (I know there is something called polytonal music, but I just wanted to make some kind of an analogy between different musical dimensions.) It's like, "now you see it, now you don't". (A great Michael Brecker record by that name btw)
Try it out yourself! :) Make a new version that goes to Dm instead of F#m. Can you make it sound believable? "Gotcha, Dm was the real tonic"? After a Dm tonic, can you make it go back so that the next Bm sounds like iv of F# minor? (Try e.g. B/C# - C#/F - F#m, or Bm6 - C#7 - F#m as a total reset.) It's all just fun trickery, playing with the listener's perception.
If we disregard the melody and how everything is done on the recording, the first part "Bm7 Gm7 Bm7 Gm7 Bm7 Gm7 F#m7" could also be alternating between D majorish and D minorish. It's common thing used in jazzy music. When there's Bm or F#m, it's on the D majorish side, and when there's a Gm chord it's on the D minorish side. But like I said, this is not the best interpretation for the functions of the chords.
You can try out the validity of the interpretations by playing solos on the chords. Then try keeping the original melody, but substitute each chord with some other chords from the supposed key.
I assume the purpose of analysis questions like this one is to achieve a practical, applicable feeling of the chords and the song, to be able to e.g. play the song more creatively and improvise on it.