I don't live in California but the article mentioned Proposition 13 which capped property tax rates and the reassessment is only when the property changes ownership?

Is that right?

That seems unfair to people who recently moved compared to the people that stay in their house for decades.

Reading more it looks like California created alternative types of property taxes like Mello-Roos.

In my state we used to have property tax values reassessed every 8 years, then they changed it to every 4 years. But my bill goes up every year. I started off paying about $2000 25 years ago and now it is about $5000 but my property value has also increased about 3X

It seems like if you just taxed an ordinary house at a percentage and you taxed a billionaire's huge house at the same percentage that you would get more money from the billionaire without needing to create special laws and special taxes.

Yup, Prop 13 is a mess and is a big part of why housing in CA is broken. But it's politically toxic to even mention substantial reform, let alone abolishing it or even just phasing it out over time.