I can’t tell you your definitions are wrong, because they are your definitions, but I can explain mine and where they come from. Your upbringing, to me, sounds like “The American Dream,” which you rightly acknowledge isn’t accessible to enough people. But to me, that sounds like what “middle class” should be. That should be where you can be if you work your job for your salary and are within the realm of the reasonable with your money. That used to be attainable on one income if you were white, but it should be accessible to basically everyone on two incomes.
I see classes less with respect to overall income distribution and more with respect to living status. It’s why terms like “the shrinking middle class” make sense. Tautologically there are as many people in the middle of the income distribution as ever, but those people aren’t living the middle class lifestyle.
So, like
Poverty: unhoused or struggling to maintain regular housing
Lower class: housed, but struggling to make ends meet. Getting by, but a big medical or other unplanned bill could have them out of doors.
Middle class: Housed and basically comfortable, often owning a home unless in very expensive markets. Can afford usual essentials and absorb some downswings. Can afford some degree of creature comforts like annual modest domestic vacations and occasional dining out.
Professional class: Usually high wage earners or business owners who have to work in their own business. Can afford nicer homes, potentially private schooling for kids, more expensive car payments, but also prone to whining about how they don’t have much money left after all they’ve spent on recurring but ultimately optional expenses.
Gentry: the lower ownership class. Owns at least one business or at least a big portfolio of stonks, although this is where many professional athletes and performers sit. Doesn’t really have to do actual work unless they want to.
Filthy rich: your multi multi millionaires and billionaires who have more money than most people would know what to do with. Generational wealth.
So, while upper middle class can reasonably describe people on the upper half but not tail of whatever the current income distribution looks like, it also means a certain life station to me, and drawing a few more lines might clear things up.
To add, obviously wealth is a continuum rather than discrete bins, and also, it’s obvious that one’s choice of place to live impacts lifestyle. I don’t really buy into the idea that a family making $250k but choosing to rent in Manhattan is “middle class,” even though their housing may mirror renters in less expensive cities. They’re clearly professional class with different buying preferences. Same if someone wants a fancier car instead of a bigger house, or to take more vacations. People may have different housing preferences within their class, but it’s more about the ability to have a certain kind of housing, and whether you’re working for someone or if you have people working for you.