But the California State government allocates the fund, right? If the state government decides where the fund goes, then can we still conclude that "the richer gets richer and the poor gets poorer" from the fact that local tax funds education?

I am assuming the state sends each school district the same amount of money per student and the local government makes up the difference. So yes it is the rich get richer and the poor get poorer.

I know in my Metro area the more affluent parts of the city, love breaking off into their own city to keep their money even more localized.

> I am assuming the state sends each school district the same amount of money

It does not, not even per pupil since there is a 20% supplement for each designated “high needs” pupil, and additional funds iif “high needs” pupils exceed a certain threshold.

> But the California State government allocates the fund, right?

It allocates the state funds that make up the vast majority of education funding among the counties. It doesn't specifically direct how counties spend the money.