Hi Stéphane,
To make a new Category, you must be in the File where your Assets are and then switch to Current File, Click the plus to make a new Category under the one where you click the plus. You can then Drag and Drop your Assets in the new Category. Don't forget to Save the changes and then Save the blend File.
So, something like this:
Is that what you were having problems with?
There might be other ways to do this, but this is how I do it and it seems to work.
Thank you very much, I’m going to test this. It could be more intuitive in my opinion. Thanks again