It moves because the dropouts are damaged or not made correctly and are not flush flat with the axle flats.
The nuts don't hold the axle in place from rotation. They just keep it on the bike.
The flats of the axles, along with the flats of the dropouts, keep the axle from rotating.
The torque arm or torque plate are just extra thickness to do the same thing, added to the dropouts.
Since the torque arm is not bolted to anything, it does not do anything but point in the direction the axle does, like a needle on a compass. You must bolt it down to the swingarm for it to prevent axle rotation.
Since the dropouts are either damaged or made wrong, they also do not do anything to keep the axle from rotating.
To fix the problem, you have to fix all these things. (not just one)
If you don't, it doesn't matter if you use regen or not, you'll eventually either break the axle or the dropouts, and the wheel will either fall off the bike and crash you, or rip the axle wiring apart and short phases together, blowing up your controller and forcing you to buy a new controller and either a new motor, or opening up the motor to replace the axle cable.
Torque washers only work if the dropouts perfectly fit the washers, and the washers perfectly fit the axle, and everything is strong enough so that none of these pieces can gouge into each other. None of those things ever happen with typical ebike stuff. Torque washers are pretty much useless for most setups above a few hundred watts (depending on the actual torque at the axle).
Also, I just noticed that the torque washer is installed with the tab to the rear, with the open end of the dropouts. This means the axle torque is prying the dropouts open with the lever the torque washer applies,so rather than helping, they're actually making the problem even worse than without them installed. If you are going to use them (which I wouldn't bother with in this case), I'd put them on with the tab facing toward the front of the dropout, which is harder to pry open. (this is why it is better to put the axle as far forward as possible, too).
Since you haven't said or shown what other hardware comes with this that you are not using, we cannot tell you anything at all about that hardware, except that it probably came with it for a reason.
Washers in general are used for a few reasons. One is to keep a nut from scarring the surface it would otherwise be directly rotating against. This is usually done with flat washers. Another is to lock a nut from rotating from vibration/etc., this is usually done with lockwashers that work in a number of ways--ridges, wedges, or dome shapes. Things that push back against hte nut when it tries to turn, helping to prevent that. They can also be used to keep the axle shoulders from digging into the surface of a softer-metal frame, or it's paint. If they dig in, they not only damage that surface, they also loosen the rest of the axle hardware because now the nuts aren't held tight against their surface, since that end of the axle has moved outward away from that surface now, since the inboard (shoulder) end has moved outward thru the surface of the dropout. There's other reasons, depending on the washer and setup, but we'd need to see exactly what you have, and whatever instructions and pictures came with the system, to try to figure out what the manufacturer intended.