Native English Speaker Here:
I don't think your worry is justified. Most people have messy kitchens after working on some culinary project. Just baking a cake can leave a mess.
Messy does not mean "unhealthy" or "disgusting", words we would use for a mess allowed to sit and draw insects or grow mold.
Usually, a "messy" kitchen is put back in order fairly quickly simply by washing up: dishes, pots, pans, bowls, counter, mixer, blender, cutting boards, stove top, whatever was used in the preparation. And of course putting away, spices, bottles, etc.
But it does provide a nice contrast, a perfect culinary work of art with all the mess that produced it in the background. Kind of messy like an artist's studio is messy.
Messy does not automatically trigger thoughts of unhealthy. It usually just implies there is some clean up to do.
As @TimothyAWiseman says in the comments, synonyms of "Messy" like "Dirty, Filthy, Grimy" do have unhealthy connotations. This answer applies to the specific word "Messy".