I'm glad and flattered you noticed! : )
I'm sure you can find details by googling, like I did, but the broad strokes are:
We used Godot, and to do the dynamic music, I used multiple AudioStreamPlayers. Each was tied to a different bus. when it was time to switch, I would get the current time of the one playing, start the new one at that time, then use a tween to turn the volume on one bus down and up on the other. It took some finagling of the different parameters of the tween to get it right, and I can hear where it's not perfect, so if I were to do it over I would just start one at max volume and stop the other, and hide the transition with some sound effect. : P