
Why does the engine recommend taking the bishop with the pawn here
I'm not very strong, but it's likely more positional in nature, opening up the g-file. Black king would likely go to h8, rook to g8, and after an f6 push, the queen will head that way.
Because otherwise white would have an eternal knight outpost on e4.
For example 14... Bxf6? 15. Ne4 and white is better because the knight is very strong in e4 and can never really be driven away and also his bishop is better than the the black bishop. Compare this with 14... gxf6! 15. Ne4 (maybe not the best move here) f5 immediately driving the knight away when black controls the centre and seems to have some advantage.