Median household incomes of the state of California and its five largest cities from https://www.census.gov/quickfacts/fact/table/fresnocitycalifornia,sanfranciscocitycalifornia,sanjosecitycalifornia,sandiegocitycalifornia,losangelescitycalifornia,ca/PST045218
$67,169 California
$54,501 Los Angeles
$71,535 San Diego
$96,662 San Jose
$96,265 San Francisco
$44,853 Fresno
$100,000 is in the upper half in all five (although just barely in San Jose and San Francisco, but closer to double the median in Los Angeles and Fresno, and about one and a half times the median statewide).
https://nces.ed.gov/collegenavigator/?q=berkeley&s=all&id=110635 and https://www.collegedata.com/en/college-profile/1090/?tab=profile-money-tab have some useful information. At UCB, we can see:
19% of frosh and 28% of all undergraduates get Pell grants. This approximates the bottom 50% of the household income distribution (around $6x,xxx and lower).
52% of frosh and 43% of all undergraduates get no grants or scholarships. About 24% of undergraduates are out-of-state, so assume that they are all or almost all in this group (and with very high income/wealth to be able to afford the out-of-state list price). That means about 19% are in-state undergraduates paying list price, which means household income over $140,000 (top ~20% income), and no merit scholarships. An additional 5% of undergraduates get merit scholarships but not need-based grants, so they can be assumed to be in the upper range (over $140,000 in-state, higher out-of-state).
We can also see that 29% of frosh and 29% of all undergraduates do not get Pell grants, but get some grants or scholarships. As noted above, about 5% get only merit based scholarships, so that makes 24% getting some need-based grants but not Pell grants.
In other words, out of all undergraduates at UCB:
28% in-state from the bottom 50% income
24% in-state from the 50th-80th percentile income
24% in-state from the top 20% income
24% out-of-state from high income
So it looks like the “upper middle class squeeze” is really coming from the top (both in-state and out-of-state), not the bottom. Note that while the 50th-80th percentile income group is somewhat underrepresented at UCB, the bottom 50% that you appear to look down on with resentment is underrepresented to a much greater level, despite any favorable looks by admission readers seeing some of them achieve despite having more obstacles and barriers.
If you look at most highly selective private universities, you will find the skew toward students from the highest income families much greater than at UCB.