Ebike brake lever cutoff switch / interrupt switch : How does it work?

In your current set up, the electric brake lever sensor will protect against the situation where you're emergency braking but forgot to release the throttle.

The brake sensors override the throttle because there's basically no reason to power the motor while braking.

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If your bike was configured to use a pedelec or pedal-assist mode, then the controller will detect when your cranks are turning, and the controller then instructs the motor what power levels to be putting out. There's generally some lag, where you have to do some rotation of the cranks before the motor starts to power you. At the other end, the same crank sensor will take a short time to decide you've stopped pedalling before it drops the motor assist.

Its conceivable that you may be braking hard, and have been riding at 60 RPM on the crank. Your feet may turn another half rotation, and then the motor takes a "missing" half rotation to decide to cut the power. That could be an entire second of time where your motor is powering you forward against the braking force, which is 7 metres at 25 km/h or about 2 car lengths.

The electric brake lever sensor should be telling the controller to STOP RIGHT NOW and override those other inputs.

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Additionally, electric brake lever sensors can be used to activate secondary electric brakes and scavenge some power back into the battery. Sometimes this simply uses the motor as a generator, and sometimes there are separate coils.

This is relatively rare on ebikes, though electric trail bikes may have this feature.

Side note - electric brakes aren't legal, and the bike still needs mechanical brakes to be on the road.