I left a comment [0] on the other thread, and this is irrelevant if you aren't using Photoshop, but there's a plugin called DITHERTONE Pro that gives you a lot of control over the dither algorithm used + color grade. For actual design, I tend to use this since I'm already in PS cobbling together an image, and you can tweak the results in realtime to dial it in how you want.

I also have used didder [1] a couple times for dithering via CLI / script. Its results can be pretty good too, just more for repeatable batch operations and you need to make sure your palettes and chosen algorithms will produce what you're actually looking for.

[0] https://news.ycombinator.com/item?id=45726845

[1] https://github.com/makew0rld/didder