You’re using a definition from a random dictionary. This is neither the original meaning of the term nor the one Marxists use. The version you looked up is a “new” bastardization of the original term.
The bourgeois class under marxism is the class that makes money by owning capital through the labor of others. Think about people who own businesses or have large investments. They don’t make all that money themselves, they make it from people who work in facilities they own.
There is something called petite bourgeois that could be called middle class. These are small business owners who both work their own business but also have employees they profit from. Marxists care about how you make money, not how much.
Glad you learned something. Normally this is where I get told that the marxist version of the term is wrong or dumb even though it’s closer to the original meaning than the modern definition.
I am sure the authors of Merriam Webster don’t mean anything harmful. Dictionaries update their definitions based on how they see the term being used, and many modern people don’t respect the original meaning of the term. In political circles we still use the original meaning. You can see why this causes confusion.