The trim motor (pdf here) drives the jack-screw through a reduction gearbox, on the side of which is the pulley for the manual (cabled) trim wheel. A torque clutch between the motor and gearbox allows the manual trim pulley to have priority in the system.
It does indeed operate at two speeds – faster with flaps down (when low speed requires faster trim movements) slower (1/3 that rate) with flaps retracted (higher airspeed assumed - smaller adjustments required)
(Edit: controlled by a speed change relay in the STM)
The slower speed is the one MCAS operates at – as MCAS only operates in manual, flaps up flight.
MCAS in operation moves the horizontal stabiliser trim .27° per second, up to 2.5° and 9.26 seconds per activation.
(Edit: and repeats after 5 seconds if activation conditions remain)
The yoke mounted electric trim switches (theoretically) move the trim at the same speed.
In comparison (I read on PPRuNe forum that) one turn of the manual wheel equals about 0.07 trim units, so requires 15 rotations per unit of trim.
So MCAS trims down at 0.27 units per second, or 3.5 rotations of the manual wheel per second.
That's a lot of manual winding to reverse every 9 second MCAS activation.
In addition, compared to earlier iterations Boeing had reduced the trim wheel size on the NG & MAX (to clear the new display panels) reducing it's mechanical advantage.