I still think it might be a mechanical problem, in particular with the worm gear to the plastic gear. Although I cannot exclude the electrical nature of the problem.
I noticed something strange at 0:20 in your video (it could be a video artifact, though). When starting the engine in the opposite direction, it looks like the plastic gear, although jerky, rotates, but the metal gear of the shredder shaft drive is practically in place. Then, when the power supply to the motor is turned off, by inertia, all the gears rotate absolutely evenly (this is less than one second, but you can see).
Based on the circuit shown on the motor, this is a single-phase motor with a starting capacitor and two (presumably the same) windings. To reverse it, I believe, the order of connecting the phase-shifting capacitor to the windings (in one direction - to one winding, in the other direction - to the other) is changed by connecting the neutral to the gray or black wire. If something is wrong with the switching circuit or with the windings themselves, this can lead to insufficient starting torque (due to current limitation, for example) or something similar. Perhaps a high starting current at the initial moment causes a voltage drop in the circuit, then the winding turns off and the current drops, then turns on again, etc. Something like that, I cannot say for sure without more detailed information, I just assume.
On the other hand, rotation of the worm gear in different directions causes different axial forces on the mating gear. That is, in one direction, the engine and the mating gear tend to be attracted, and in the other - to push off each other (something like that). Alternatively, check if the bolts securing the motor to the frame are tight.
I can suggest as an option, in order to determine if the problem is caused by the control electronics, temporarily swap the gray and black wires according to the diagram on the motor. In this case, when the forward button is pressed, the motor will rotate in the opposite direction, connected through the commutation elements of the forward direction of rotation. But before doing this, MAKE SURE that my assumption about the reverse circuit of this motor is correct. There is a fuse on the white wire according to the diagram, so I assumed that this is a common wire.