You should still get a W-2, as you will still have to pay FICA and Medicare. The exclusions are only for State and Federal Income Tax purposes. The W2 can then be used to qualify for the earned income credit (EIC) or the additional child tax credit (ACTC), as well as other services, including Cal-Fresh, etc.
https://www.cdss.ca.gov/inforesources/ihss/live-in-provider-self-certification
Live-in provider self-certification
https://www.cdss.ca.gov/Portals/9/FMUForms/Q-T/SOC2298.pdf
SOC 2298 (ca.gov)
