Parts that have not been modified by me are available for download directly from the designer
https://www.thingiverse.com/thing:3577666

new Gearbox.

Sprockets_n_Shafts_Hodor
Shaft_Hodor_Right
Helical_Gear_Left/Right
Worm_Shaft_Left/Right

Using a worm gear with a small reduction factor, I was able to increase the opening/closing speed x4.
Sprockets_n_Shafts_Hodor and Shaft_Hodor_Right minimize the distance between the Helical_Gear and Worm_Shaft.
Sprockets_n_Shafts_Hodor also got a notch for wires between Arduino and the motor controller.

As a stepper motor driver I use A4988. Connection diagrams can be found on the network. 28BYJ-48 has more power.

new Window Hodor

Window_Hodor
Latch

The new Window_Hodor does not require making a hole in the window and can coexist with the roller blind cassette.

new Casing

Base_End_Left/Right
End_Cover_Left/Right
Base_Cover_Left/Right
Window_Frame_Hodor_Left/Right

Base_End together with End_Cover includes space for Arduino, 2x power connector, motor, motor controller and LED.
Base_Cover looks better over the entire width as two halves.
I've given up the middle Window_Frame_Hodor. Window_Frame_Hodor_Left/Right support the whole mechanism sufficiently, which allowed to reduce the number of holes in the window frame to two pieces.

2x DC power socket, because the device can be powered from different sides.