I do not remember why I decided to try my luck and see if anyone online figured out how to make custom screensavers for the kobo e-readers but I am glad I did.
I almost did not want to get a used Aura HD for a low price because this feature did not exist and there were no hacks at the time.
many thanks frostschutz,

your procedure was successful on my Aura HD with firmware 3.18.0.
I used the scanline method of course and here are my results that I got with the debug:
offset=145
standby=e3b115f0c3e42bcef1afcbbb4f10e6da
poweroff=62aed5baa23b6f925d79d836b221ebf5
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I hope to contribute something in regards to creating optimal images for use on at least the kobo Aura HD. I do not know which other devices share identical screen characteristics.
I used to have a kindle 3rd gen. Before it broke I almost perfected the art of creating wallpaper files. I made a custom PNG profile in photoshop to export as a greyscale with 8 levels, and I set each level manually once based on the kindles 8 level screen.
the Aura HD screen is listed as having 16 levels on wikipedia. I loaded a gradient from white to black (which I assume photoshop makes linear) as the only image and noticed that the kobo does not dither the image, but instead has a hard sampling a.k.a. quantization technique. I notice very equal spacing between each sample. If the original gradient is linear than the quantization is linear.
I applied a 2 different 16 level ditherings to the gradient with photoshop and loaded those images to inspect them.
one of the ditherings photoshop used its own algorithm.
for the other one, I manually chose the greys from 8-248 in steps of 16, so: {8,24,32,...,232,248}
I attached files for all of these examples.
my conclusion is that a linear levels for dithering is not ideal. there are uneven bands on the Aura HDs screen but not on my computer monitors from both dithered images.
That being said any type of dithering gives a huge improvement in the perceived image quality.
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I will also share show I save my images.
I only use photoshop, perhaps there is an equivalent procedure in GIMP, I do not know.
-first I get a high res image of course,
-crop it to 3:4 ratio
-(edit) select auto contrast or use curves manually to get some clipping into the black and white
-sharpen if needed
-if it's a color image, I go to: image > adjustments > black and white. then I play with the presets until I find something I like and then maybe tweak it from there.
(this control can give significantly better results than simply desaturating)
-resize to 1080x1440
-file > save for web. then choose PNG-8, 16 colors, adaptive mapping, 100% dither.
-save
I have included a screenshot of some dithering comparisons
top left is the original image
top right is 100% dithered with my 16 level profile
bottom left is 100% dithered with an auto 16 level profile
bottom right is 0% dithered with an auto 16 level profile (somewhat how the aura hd would show the image itself based on the gradient test)
my profile does look better on the PC screen but if the results of the gradient test repeat then it might not translate to a better image on the aura. but the difference is negligible in a more detailed area anyway.
for me the hardest part is choosing what images to use. I have made 4 so far and I can share a live folder if anyone wants.
hows that for a first post?