I think getting into the weeds on whether $80k or $100k or $120k/yr is a middle class sort of misses the point, but at least with my eyes it is hard to argue you're middle class if you're making more than about $150k at the most.
Even the GP, which I directionally agree with, says "upper-middle class is people making ~$200k/yr" but you're deep into the top quintile by that point, probably top 10%. I don't know what percentile I consider "upper middle" but it's definitely lower than top 10%.
A good indicator that someone is simply being dogmatic and not arguing in good faith (e.g. actually trying to understand someone's POV, and being open to being proven wrong in their assumptions) is when it takes them 5-20 minutes to reply until a particularly good point is made and then they disappear into the ether.
I didn't say A means B 100% of the time, just that it's an indicator. The same way having a car with a lot of dings and scratches and holes doesn't mean you're a bad driver, you could have just purchased it that way or they could have happened through no fault of your own. But it's still an indicator - one piece of evidence to be looked at holistically.
But I notice you haven't actually responded to the point that "the 1%" actually does mean "your neighbor with a nice house and a pool" because $800k income puts you in the 1%. That's two doctors in not-particularly-highly-paid specialties. That's two good attorneys at big firms. That's two FAANG software engineers. Definitionally there's not going to be a ton of people in that group, it's hard to get into that group, but they're everywhere not just billionaires twirling their mustache and trying to reroute rivers to sell the water like some caricature.
Upper-middle class is people making ~$200k/year.
A lot of people have moved from middle class to upper middle class over the last decade. Both those categories are outside the 1%.