While I agree with your reasoning, I think the generally accepted understanding of "working class" is of skilled and unskilled laborers that are distinct from the "professional class" that tend to work in offices and don't work so much with their hands. A plumber running a small business employing other plumbers with a massive cash assets could be a lot farther from being homeless than a senior lawyer with multiple houses and expensive cars but the plumber will always be perceived as "working class" in contrast to the lawyer's "professional class".

Social class defined by economic relations has material consequences that exist between countries and cultures, and the colloquial usage you're referring to[1] is dependent on where you are and who you ask.

To sociologists, economists, and academia, those who rely on a salary or wage to live are considered working class compared to those who don't.

[1] https://en.wikipedia.org/wiki/Working_class#Definitions

I suspect this forum has an (relatively) high ratio of people who can and do manage to do exactly that.

That's not true. With a six figure income, you can live like people making half what you do, save the other half of your income and retire early to live off your assets indefinitely. That's harder to do the lower your income gets.

No. If that were the case, then some banker in NYC, making $1M a year, but no savings, living in a $2M condo with a $10,000 monthly mortgage and 3 kids in private school would be "working class".

That's a perversion of the definition.

And a 65 year old alabamian plumber living off his meager trade union pension would be upper class.

You might find Me Money Mustache [0] interesting.

[0] https://www.mrmoneymustache.com/blog/