If you're going to crochet the result, I don't think you really want 256 colors. A 16 color pallete is probably acheivable if annoying.
Seems like if you print the image, then print a grid on a transparency sheet, you could mark up the sheet with colors until it looks good.
Maybe tracing paper (can you print a grid on tracing paper? Do you want to hand mark a grid on tracing paper?)
I don't use art tools, but you should be able to do something in software too, layer the grid on top, leave it transparent to the image until you pick a color for each square.
Drawing grids over an image is easy. Choosing which colour to drop in is impossibly hard and where the art is. Nearest Neighbour and Average of N Points are some algorithms than can be used but don’t take the overall style of the image into account. For example, one pixel could cover a part of the nose and a part of the eye and averaging them makes a blurry mess.
Problem is that like vector fonts without hinting, naive automatic "pixelation" of images does a poor job. You have to work with the limitations of the medium, and sometimes it entails drawing something in a very different shape than if you had more resolution and color. There are image gen models that do an okay job at pixel art these days though.
My wife likes to take images and crochet them into tapestry/blankets/cozies.
It seems to me that if we could get a grid overlay onto an image she could then make whatever she wanted. (One color per 'pixel')