How did you get to this result ? (I'm not claiming this is the real look it will have, simply wanted to check the metodology) Simply counting the number of colors in the image does not seem a good idea since even with a real photo, a screen with all pixels outputing the same will not give you a single-color image when captured with a camera. The issue is even worse with e-ink due to their technology.

I saved the image and cut out everything but the flowers. Then used this online tool https://www.imgonline.com.ua/eng/unique-colors-number.php

It's probably a simple photoshop as the image even seems to be higher resolution than the hardware.

But counting unique pixel colors in a photo of a display tells you nothing about the display.

Find a picture of a gameboy screen (10 colors) or gameboy color (56 colors) and send the jpg through that tool. You should be able to realize the problem from simple intuition about what a photo is.

I thought it was a mockup. If it was a mockup it should be limited to the colors available right?

I agree with the conclusion but how did you do your calculation? If you take a picture of a 16 colors screen you will find many more colors in that picture (main reason being that pixels won't align perfectly).

I saved the image and cut out everything but the flowers. Then used this online tool https://www.imgonline.com.ua/eng/unique-colors-number.php