What is the most usable method to upload single or multiple files which relate to specific categories or fields?
Of course there is no right answer. Depends of process that people follow. Its even not about answer, but about right questions. Ask yourself right questions and it will be clear how upload form should look like.
Check following 3 cases. Each one is about uploading something. But upload form will be absolutely different for each case because of process.
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How many documents whould I upload at a time on this page? Is it a document I've just created or some photos I want to share, wich are ones of a thousands? How large files could be? How many fields and categoris you have? Are files somehow related to each other? Can category be empty? Will I have to reupload file if it is a document and I found an error?
Wrong category in scenario B
What if I uploaded a 10M file over mobile internet and found out I uploaded it to a wrong category? Right. With such UI I have to reupload it again. Pain.
Drag-n-drop and older people
Dragging is something, that is totally unclear for older people. One may ask "How do I upload it? there is no familiar upload button". Do you have to take older people into account?
Making it look like something clickable like button in general is a good idea.
So what to do?
First, ask your users how they upload files and what is the process and goal of uploading.
As a starting point, your (A) option is better, since it allows user to change category after upload where (B) is not (if it matters)