how does this work with for example net worth... is class c…

No, class is just whether you benefit more from or pay more into the tax system. You can be wealthy or poor and still be upper or lower class.

It seems pretty counter-intuitive in a capitalist society to label a welfare recipient higher class than a multi-millionaire business owner

That's just because the Marxist way of thinking has pervaded everything. Class is like classification--it's just a way of dividing people that sheds light on our sociology. Does separating people in terms of wealth do that? I would argue that no, it does not and that what the mainstream media calls the "lower class" has a lot more in common with what they would call the "lower class" than the "middle class" has with either of them. I see leftism as an alliance of the "lower class" and "upper class" against the "middle class" and I call these two groups upper and lower class, in accordance with libertarian class theory.