Bad faith insurance claim in California?

My aunt was in a car accident (not her fault) in July 2023, in Burbank, California. She sought immediate medical attention and it was clear the other party was wrong and their insurance would handle the case. The insurance company is Interinsurance Exchange of the Automobile Club (AAA).

She received several months' of treatment and earlier this year was ready to settle. I helped her draft a demand letter which was sent March 23, 2024. Since then, the claim has been passed around from adjuster to adjuster (she's on her FIFTH adjuster at this point). It takes weeks for them to send an update. And each time they say they need one more authorization form or they are waiting on some third-party vendor to review the documents or medical records or some other excuse. We both have left voicemails and emails that go unanswered. Sometimes they say "we will have an update in a couple weeks" but they never come back with anything. We are at our wit's end.

Does this qualify for a bad faith lawsuit? I have to believe there is some legal protection in place for this sort of thing. At this point we are ready to hire a lawyer, but my aunt is very poor and the ones she's contacted say they work on billed time rather than a percentage of the settlement.

What are our options? Thanks.