I can't resist picking this apart some more

But our numbers for capital income are probably greatly exaggerated, because capital income gets taxed at a lower rate than labor income. Smith et al. (2019) find that most rich Americans get a lot of their income from working at their own pass-through businesses, but classify most of this as business income in order to pay a lower tax rate

This is super misleading. He makes it sound like this income is from self-employed people, independent contractors classifying their work as a single-employee business for tax purposes. But, If you read the study he cites what you find is that these pass-through businesses are still ultimately paying their owners from profits. They have employees. The difference between them and a public corporation is that they're owner-managed instead of hiring a corporate suite. This is like saying CEOs technically earn some large percentage of their income through a salary and bonuses, so they're part of the working class

The study makes an interesting point in showing that these businesses tend to fail when the owner dies or retires, but they make no claim that this is because the owner was doing enough work to constitute all of, of even a majority of the firm's revenue, just that their management was part of the firm's success. They acknowledge that

Owner charisma or connections may have kept key employees at the firm until her death. Or a firm could replace its dead owner-manager (compensated in profits) with a hired nonowner manager (compensated in wages), yielding a decline in measured profits. In each case, the withdrawal of the owner’s human capital caused profits to decline

That isn't working class Noah.