So, where do we actually see “experienced” rate hikes or dropped coverage?
Based on what’s publicly visible:

Clear resident claims of already-experienced impacts

• La Mesa, CA (EnerSmart BESS at 8135 El Paso St) Petitioners note they are in a high-fire neighborhood where homeowners’ premiums have already risen and some policies have been cancelled, and they use this as a core argument against putting a company-owned battery facility right next to homes, a gas station, and a school.  This is the cleanest, on-the-record example of residents saying: “We’re already getting hit on insurance; a BESS in a residential block will worsen that risk.”
• Eden Valley / Harmony Grove (Escondido/San Marcos, CA) – AES  Seguro Storage Project: AES’s “Seguro Energy Storage Project”: 320–400 MW BESS on ~22.5 acres near Escondido/San Marcos in San Diego County, in a semi-rural residential area (Eden Valley / Harmony Grove). AES would own and operate it.  Resident experience and claims: Local opposition groups and Facebook posts about “Stop the Seguro BESS” say that, as the home-insurance market pulls back in California, homeowners roughly a mile from the proposed Seguro site are already paying up to USD 10,000 per year in home insurance premiums. They explicitly connect this to insurers’ fear of fire risk and the prospect of a massive BESS nearby.  In a Santa Fe County meeting about a different AES project (Rancho Viejo Solar + storage), a resident asked whether their homeowners insurance might increase or be cancelled because of proximity to solar + BESS; AES responded that they were not aware of such cases for homes near utility-scale solar+storage.