Non-profit organizations generally don't focus on profits, but they are usually classified as "businesses."

I suppose this is a matter of definitions. What do you define as a "business?"

What businesses are profit-driven? I would love to know so I can avoid them.

Every gas station, grocery store, convenience store, pharmacy, urgent care, every bank, every tech company, every computer manufacturer, most food production companies, most farms, every resource extraction company, every manufacturing company.

Any health care organization - from your list, pharmacies and urgent care - that is profit-driven is not holding health as top priority.

If an organization that should be focused on making people healthy is instead focused on how many currency units it can extract from other entities, there is (as they say) a misalignment of priorities.

Every nonprofit.