Thanks for explaining!
Though to be clear, most of what I explained still applies: if you are looking to buy real estate, the expected burden of property taxes will already be baked into the market price. Almost no matter how the taxes are set.
My observation is that the system is neither regressive nor progressive for people who don't already own a home.
Renters basically don't see this tax at all, and people who are considering buying a home see the same total burden of tax plus mortgage payments.
(Or for people who buy outright with spare cash instead of a mortgage, the constant burden is tax plus opportunity cost of capital.
A mortgage is just a way to rent some capital from a bank in return for compensating them for the opportunity cost.)