>>33085318>the color of the pixels is an innate part of that imageIt's literally not, in the game's code. To use the GB games as an example since it's the simplest, you have a group of pixels that are color 1, color 2, color 3, and color 4. Color 1 and 2 are hardcoded in the ROM to always be white (a.k.a. transparent, since there's a white background) and black, and the other two colors are defined in a section of the ROM unrelated to the sprite.
This is the palette data from the disassembly of Pokémon Red. It's entirely separate from the sprite data, and you could change those palettes without affecting the sprites at all. Crystal is the same, except each Pokémon's palette is decided on an individual basis instead of picking from a handful of presets.