Interesting, yes! Your disk seems to be rotating the wrong way. The logo/print is facing right, it should be facing left, as it is on bikes with the disk on the left side. There usually is a rotation indicator arrow printed on the disk, if you find that you can confirm.

I expect no difference in braking power, and I also think the aerodynamics difference, if any at all, will be very very tiny. The concern here is that the disk is designed to take force in one direction. We do very little braking while rolling backwards, after all. If you load it in the wrong direction, you increase the chance of disk collapse, which at best would mean loosing all brake power, and at worst would lock up the front wheel instantly - hard crash.

The risk for this depends on the design. Your disk looks quite strong to me. It has not many holes in the surface and the black carrier makes it stiff. And it is not as extremely spiral shaped as some other designs are. Compare to this light weight one piece design. Loading this in the wrong direction would be more dangerous than with yours, I think. Still, it's a risk I would not take, personally.


Light weight disk

Simple one piece designs are fine to flip over because they are flat. The surface doesn't change sideways position when you flip it. But with multi piece designs that can happen. The black carrier material may be thicker than the brake surface. If so, when you flip it the surface now has moved outwards, and doesn't fit the position of the brake caliper anymore. Maybe it's an insignificant effect, maybe not. Regardless, for safety I will use a reputable brand rotor mounted in the correct rotational direction. I don't see any benefit with fancy multi piece designs that outweigh the risk. If you can flip a multi piece design like yours without caliper alignment trouble, it should be fine.

You must be right about the folding as the reason why the Birdy disk is set up this way. It seems an unintended consequence of a bike originally designed for rim brakes. The other peculiarity, that the disk is mounted closer to the center of the wheel and requiring special hubs, must be for the same reason. Likely the fork swingarm would have to be made wider if they where going to use standard hubs. It could also be that the hubs are also designed to take brake force in one direction, so they would need special hubs anyway. Dynamo hubs could also be most efficient in the correct rotation direction, I don't know.