Yeah that’s odd that it works on single player but not when installed as a mod.
You only need to move files into the folder that you modify, not the ones you’re just using. For example if you make a custom map and paint it with beach sand texture you only need to have the map files in your mod folder, not the beach sand texture.
If you said “you know, I like this beach sand but I want it to be a bit darker…” and you modified the beach sand texture you would then need to copy one to your mod folder, edit that one, and reference it.
Eg, Copy beach sand texture to mod folder -> name texture file TuskonysBeachSand -> edit new texture -> paint terrain with reference to TuskonysBeachSand
But I don’t know if having extra files in your mod folder will effect the outcome of the map cooking.