Processing is open source, so you can see exactly what it does with the colorMode() function. I would take a look here:
Specifically check out the colorMode() and colorCalc() functions. It looks like the colors are stored as individual R, G, and B values, as both float and ints. Then those values are used in a more specific type, like this one:
Basically I’m not sure how much value you’d get from trying to store the internal color as a single byte. You might represent it that way in your sketch, but then do the conversion to normal R, G, B values before you use any Processing function.