Correct. And AE is most of that $2.4 billion, at $1.86 billion. San Antonio, on the other hand, does NOT include CPS's total budget in its city budget (it just includes the transfer made to the city by CPS).
So, if you want to do an apples-to-apples comparison (both budgets without the expense side of the electric utility, you're closer to the comparison you cite. There are certainly numerous reasons why the Austin budget on a per capita basis is higher than SA's, but that doesn't account for all of it, by far. That is, the per capita budget delta isn't entirely on city government.....but a good chunk of it IS on them.
It's not just that Austin hasn't done a great job at managing its budget though (that's a big part of it). Rather, a big takeaway here is that....drumroll....San Antonio is actually one of the best-run cities in the state, probably by far the best run of the large cities. Seriously, lots of folks should look at how SA does things and say "we should do more of that." Nobody's perfect, of course, but SA does things better than most.