This Lupine light needs about 10 W so no problem tu use directly the motor output.
4'000 lm, it would be closer to 50 W, way too much for this same output. So, again, you need to connect it directly to the battery. External or internal battery is a non-issue.
This is NOT supplied by the 6V (12V) output of the motor.
The main power comes from the battery and the motor output should be used as the switch.
Depending on the input circuit, it may work with an 8.4V battery pack.
It won't work with a 8.4V light and the output won't supply enough current.
With Bosch CX motor, your shop can change the output to 12V so in the end 12V and 1.5A for 18W. Anything more and you need a direct connection to the battery.
These look nice and the price reflects this...
The "issue"...
The efficiency should be pretty similar for all motors. And for the torque, with the power and the cadence, you already have it: Torque = Power / rotational speed.
I would be interested to see the evidence you have. But many things are possible outside of the motor and for this part I have no doubt.
I still think it's just a Brose motor with a Specialized sticker.
Not so sure about that. In the past everything look like it was a "standard" motor and they add a layer in the battery management for the communication and parameters access. I would think it's still the same.