You're not conceptually wrong, but structurally, jeffbee is quite correct: the details vary from state to state (for the exact same reason: every state has its own constitution describing how it is organized separate from the federal government) but unless that constitution says otherwise, the governmental structure of the United States is (right there in the name) a union of states, and each state has (federally-constrained) sovereignty in its borders.

If the California constitution says cities have more power, then they do. But I'm pretty sure it says (like every state constitution I'm familiar with) that city power is wholly defined by state authority and if the state wants to explicitly revoke the right to zone, they can do that.

(Whether or not it's a bad idea is independent of the question "Do they have the authority").

So what?

The constitution of the U.S., and likely of every State, clearly does not endow any independent sovereignty to local municipalities.