Importing fbx with embedded textures, pipeline question

Hello there! I've spent a week trying to import my textured model from Blender to Unity. Seen lots of tutors, read lots of texts. They all suggest to click "extract textures" button in materials tab of fbx file in unity. But when I click it and choose target folder, nothing happens. Folder is empty, texture is not extracted. Fbx DO have texture in it, I see it in windows 3d viewer.

I saw people in youtube who create huge games in unity with tons of objects and I wonder if they struggle with importing like this? Why such a basic operation (importing model) is so complicated? Do they do it by exporting mesh and png of texture separately? For each of hundreds of models?

What is proper way to work with models?
Maybe I should do texturing in Unity? Blender is for modelling only?

Here is my fbx with empty texture:


Thanks!