Nor is a union the economic or legal definition of a cartel. A union is closer to creating a company that acts as a negotiating and protective apparatus for its employees as they do contractual work for other companies.
That isn’t a cartel and there can be multiple, competing unions working for the same type of workers in the same industry.
an association of manufacturers or suppliers with the purpose of maintaining prices at a high level
That's the definition of cartel. Unions exist to maximize the amount they extract from buyers of labor. This is rent seeking plain and simple.
What's more, they don't compete with each other, which is what corporations must do. Why does the UAW get to enjoy a monopoly on the sale of autoworker labor? Should Ford and GM and Chrysler be able to unionize together to keep wage costs lower?
That isn’t a cartel and there can be multiple, competing unions working for the same type of workers in the same industry.