Can I include Business Categories in the Budget

The short answer is no.

The budget is a part of the program which is purely for personal categories, and Microsoft have made it so that categories for business purposes cannot be included. In addtion, business accounts cannot be included in the budget too.

If you want to be able to put business details in the budget, perhaps you could lobby Microsoft with a wish, but I wouldn't expect this one to get implemented in the short or medium term.