You should have as many as you need. Do not create categories if there are no articles you can place within them. But do not group unrelated articles under the same category. Check into some keyword research to see if your broader categories get search volume and go from there.

For the example you gave, I would say to keep them all under a "branding" category and expand into those other keywords through articles.

If you have a more broad category it may get linked to more since it has more articles people may want. Therefore increasing its PA and ranks

I just turned off AIO. I prefer it for titles and stuff. But yoast had the rel canonical function that I needed. I wish there was a way to turn off parts of yoast