I'm a licensed civil engineer in California, and I don't think the answer is a black and white yes or no. My civil license allows me to supervise and/or stamp work that I have taken personal responsibility for. It allows me to stamp only work that I have direct work experience in. I have no specific seismic experience, for example, so I'm not legally allowed to stamp and work with seismic calculations, even though that work rightly falls under civil engineering. Likewise, I'm not aware of any regulation in the Business and Professions Code that might prevent me from stamping work that might be considered mechanical engineering, if I can show relevant and recent experience in that field. In fact, I've done some pump station work in the past, which is just as much a mechanical discipline as a civil one. (Ironically, my engineering degree is mechanical, not civil). Most, if not all public agencies do require a registered civil engineer's stamp for public works type projects, but that is up to the agency, not part of the state regulations. That might also be true for agency contracts for mechanical/structural type work as well. But that would be a separate agency requirement, not a state regulation. FEA is most certainly as much a mechanical discipline as anything else, so I suspect you'd be fine doing that work with a mechanical license.
My advice would be to read the Business and Professions Code for Professional Engineers available at the state's website. This is a good place to start: https://www.bpelsg.ca.gov/laws/pe_act.pdf If you need to ask a specific question to someone at the state level, you could start here: https://www.bpelsg.ca.gov/ There are also professional engineering associations around the state that might also give you good guidance. All of the above is from my memory so take it with a grain of salt, and good luck!