Depends on how heavily it's raining and the temperature.

Light sprinkle and warmer weather (not by California standards - I spent most of my adult life in Colorado with real cold; this means 55-60ish) implies shorts, jersey, and an Arkel Commuter pannier.

Heavy rain and/or cooler temperatures progressively add a rain cover for the Arkel (it does a fine job keeping moisture out, although I love my carpet and would like to leave the road dirt at the door when I come inside), jacket, shoe covers (I hate soggy socks and wet feet), rain jacket replacing the jacket (I used to have a nice performance brand Gortex jacket with mesh lining, pit zips, and a vent in back in which I stayed dry and did not roast; although the current unlined Gortex jacket with only pit zips isn't as nice)/pants, and gloves. When I lived someplace cold I sometimes used a helmet cover.

The bike goes inside regardless.

When I was young I lived in an alpine dessert where fenders rarely mattered and I didn't care otherwise; approaching middle age with wetter winters I want some fenders and will probably build a titanium or stainless frame with clearance and longer chain stays once cash flow is better with the kids moving past their odyssey years.