Prop 13 still applies (though I personally think it inflates home prices in CA above their "true" market value and disincentivizes anyone from selling/moving).

When I bought my home this year, it got re-assessed at my purchase price, yes. But for as long as Prop 13 is the law of the land, no matter how much home prices in CA inflate, my property tax is more or less capped at the price I paid for the house.