Is this a draw or win with perfect play?

Draw - Black wont be able to take control of d2 and won't be able to promote his g pawn successfully as long as the dark squared bishop is on the board.

Black could perhaps try playing Ke6 bishop somewhere (f5,f6,h7 depending on the conrete variations) and then d4 with the idea to gain some entry route for the king (via d5,e4,f3 for example). I'm not sure if this actually wins as I haven't done any deeper analysis but it feels promissing.

I'm pretty sure black can escort the g4 pawn - i.e., Kf6, Kg5, then white's either going to lose his bishop or his king will have to be in 2 places at once.  I really think black can win, but I'd have to play it out to be sure...

It's nearly impossible to cause a zugzweng on boards w/ opposite colored bishops. There doesn't appear to be anyway to tie down both the black bishop and king from moving at the same time.

In this type of endgame, the king is the most powerful piece, and the bishop is simply a defender. You really need to force a zugzweng in order to win, but with opposite colored bishops that is nearly impossible.

The best chance is to stack pawns on d3 and d4, so you can control the e3 and f3 dark squares. This will take mobility away from the black king. Then I recommend advancing the king up to e4. If you can do this, you might be able to force a zugzweng.

The correct answer is that black wins because I (playing white) got disconnected by a bad internet connection and forfeit :)

I was convinced it was a draw, but now that I've had a chance to look at it with fresh eyes, I'm thinking it's a win for black.

As someone said earlier, the black bishop can move out of the way and allow the king to advance to e4 and then f3, from which he can escort the g pawn and win the bishop for that pawn.  From there he comes back and should win fairly easily with the extra pawns and the bishop that controls the promotion square.

you should think about how to improve your play so you don't get into such inferior positions, if i were you i would look what mistakes i did in opening and middle game.

I don't see a way for black to put white in zug here. I would say it's a draw with perfect play. The black king definitely cannot escort the g-pawn, and the only way to get the black king to e4 is by giving up the d3 pawn, which would also end up in a draw.

Very interesting postion. Looks like a draw to me.

Draw.

This should reduce two a center + knight pawn opposite color bishops ending which is drawn if the defender knows what to do.  In practical sub-master level play black has very good chances.

I agree

I think this is very crucial bit of information. I now believe that this position should be drawn because of this teoreticaly drawn ending. Here is an illustrative variation.