When we speak of pottery as a hobby, we think of handling clay, sitting in front of a pottery wheel, choosing a fitting glaze, then admiring our finished work. The focus is on exploring and enjoying the process. You have complete control over the process and you can do as much or as little as you like because there is no delivery pressure. Sounds fun!
But a pottery business is a different beast. Now, the act of making the pottery is a much smaller part of the overall workload. You have to deal with marketing, sales, payments, inventory, and communications. Your pottery time is no longer about exploring, but about replenishing inventory or handling custom orders in time to avoid bad reviews. You can't just make a piece and be done with it, you have to carefully pack it, handling shipping, drop it off, and hope that nothing goes wrong. If it does go wrong, you now have to deal with the fallout and handle angry customers. Most customers are fine, but it only takes 1 irrationally outraged customer to ruin your day.
Hobbies, by definition, can't be a job. You can try to make a job or business that includes your hobby, but it's a superset of the hobby with numerous other activities that you may or may not enjoy.
I do actually know a lot of people who enjoy running businesses. You might say that businesses are their hobby and delivering results to customers is their passion. Not surprisingly, they're doing quite well in both business and the mental health department. Lucky.