Teacher looking to expand, question about when I need to become a business

Currently teaching a local course in Ohio with between 20-40 students per year. Although I handle every aspect of the course, it's contracted through a local non-profit org.

I'm looking to expand my course online through a website called Teachable (or some other alternative as I haven't tested it out yet) so I can bring in students from across the country.

The goal is to eventually have my own website and not rely on any other organization or company to help support my courses.

What I am wondering is when I need to think about applying to become an actual business. While I'm teaching on Teachable or some other online teaching template, I'll be making my own income yet I'll be doing through that website which is it's own company. So I assume I won't need to do it while I'm on there. However, when I make my own website and out on my own, what threshold is there that I need to cross before I apply to become a business?

Is there like a certain amount of income I need to bring in before I have to become a business? Or is there some other requirements that I must meet before I need to apply to become a business? I tried to google but it seems hard to find the exact information I'm looking for.

Thanks!