Commercial property in California for whatever reason is also covered by Prop 13, so the property tax increases are limited. A large retailer of Costco or Walmart variety is able to move the needle as far as the underlying property valuation, which is why they typically assure a tax break before they even consider development. If the commercial property is owned by a REIT, and the retailer carries a long-term lease, the REIT as the landlord is covered by Prop 13 as far as potential valuation volatility goes.
There's a cut of the sales tax revenue that municipality gets, but commercial projects like shopping plazas also require significant municipal spending as far as the roads, street lights, infrastructure hookups, etc.
I live in Southern California which has a sprinkle of small towns packed into a limited space, with a new town forming through annexation every few years or so. Some towns are very commerce-friendly, some are very unfriendly. You'd assume that towns with a large retail presence are swimming in cash, while those that are mainly residential have a Prop 13-caused budget crisis any time they need to replace a light bulb in a street light, but it's not the case.
There are some very rich (as far as cash flow statements and balance sheets) towns that are purely residential and there are very poor towns with significant shopping and industrial presence, as well as the opposites of those two.