Exactly. In other words, especially where supply is constrained, the property tax is incident on the landowner rather than the tenant.
> my take on that is that's more caused by NIMBYism and an unwillingness to build enough housing to meet demand
Yes, the difference in land use is bigger than the difference in tax rates. However, when property taxes are higher, there is more incentive for cities and households to allow more housing. And even if you believe that property taxes are regressive, it should give you pause to realize that it is more than made up for by California’s bad land use restrictions.
> Property tax is absolutely not a progressive tax, by definition: everyone pays the same rate based on the value of their home, not based on their income or means.
No, that’s just who writes the check. You had it right the first time. The tax incidence is who bears the burden of the tax. Since property taxes are capitalized into the price and the supply is not very elastic, an increase in projected tax payments (due to an increasing rate or increasing property value) are largely borne by the landowner (in the form of a lower sales price or a sales price that grows more slowly) rather than the young worker who buys/rents it.