It even runs without any electrical power from the e-bike, since the shifting is performed inertially instead of using an input loop based on a speed sensor.
Oh man, I have some mixed feelings about this. The first few iterations of automatic transmissions for automobiles (circa 1970s I think?) also used mechanical means for shifting, somewhat similar to centrifugal governors. While they did remove the need to manually shift, my understanding is that they were also not exactly predictable. And since automatic transmissions wouldn't be very useful in performance cars, they would have found use in mid-tier cars with mid-tier performance. So a mis-shift would leave the driver poorly configured if, say, they're trying to accelerate to merge onto a highway.
For 250 W ebikes limited to 25 kph (15 MPH), this might be less of an issue, but I hope that Bafang can skip over that part of automotive history and that it Just Works(tm) for typical human pedaling cadences.
In that regard, the calculus should be simpler because the "dynamic range" of pedaling cadences is only some 50-200 RPM, or 4x between slowest and faster. Whereas for automobile engine speeds, the range can be 700-7000 RPM, or 10x between slowest and fastest. And even if Bafang sets the gear ratios consistently too high or too low, the sprocket ratios of the chain/belt can be used to tune that linearly. So bike manufacturers should have a number of parameters they can tweak, for either leisure- or commuter-oriented product lines.