In printing with an engraved plate the ink is spread out over the engraving and then the surface of the plate is wiped with a rag.

The printed image is a result of the ink that remained in the etched grooves without being wiped off. I don't see any way you could mix colors on a single plate without it becoming a blurry mess.

I'm thinking maybe the outlines were printed in a single color and then the colors were hand-painted in the book itself, sort of like 'paint by numbers.'

https://www.finerareprints.com/blog-and-tips-about-antique-p...

I can't find anything about printing color with engravings pre-lithography other than 'they painted in the color.'