The one thing I'd dispute is

The modern day "middle class," which another commenter rightly describes as the "petit bourgeois,"

As you correctly identify in your last paragraph, class is defined by your relationship to labour and the means of production, and not strictly related to how much money you have. The petit bourgeois may generally be what we commonly think of as middle class, but it more specifically refers to small business owners. People who make money from the labour of others, but still have to do real work themselves in order to maintain it. A doctor at a hospital is not petit bourgeois, but a doctor running their own clinic and employing a nurse and a secretary is, and would be even if they had less income. Even a sports player who makes tens of millions is not really petit bourgeois or bourgeois if that's all they do - although they often go in that direction after some time.

Where it gets complicated in our financialised world is that our savings, if we have any, are often invested in corporations, and after a lifetime of working for a decent wage, some of us are fortunate enough to be able to live out our last decades or years from investment income. It feels a bit tough to describe retirees as bourgeois even though by the strict definition that would be the case.

Despite this complication, I think it's much clearer to think of class distinction in terms of the relationship to work, as this is what mainly incentivises attitudes to political and economic policy. If you get your income from other people working for you, you're more likely to want to drive wages down and not pay for healthcare. If you get paid for working, you're more likely to want wages to increase, even if your wage is already high.