If Santa Cruz is a STATE Beach (not a city beach) then no, you are not allowed to operate your drone on the state beach property.
While drones are not banned in ALL state parks, the superintendent of the Bay Area State Parks has banned drones in all of the Bay Area state parks EXCEPT for Airplane Hill at Mt. Tamalpais State Park.
https://www.parks.ca.gov/pages/519/files/BAD_PO_Model_Aircraft__UAS_Glider_Use.pdf
That news article you linked to says that Seacliff State Beach allows drones, but I would double check with the district that overseas Seacliff State Beach to confirm.
Remember though that it bans operating the drone ON THE BEACH PROPERTY, but not ABOVE the beach property. So, if Santa Cruz city allows you to operate your drone on private property, you could stand on private property and fly OVER the state beach. Just can't stand ON the beach.
But Santa Cruz might have other requirements for operating a drone in town. Plus, as you know, federal regulations prevent you from flying over people, and if you plan on filming then you MIGHT need to have your 107 certificate and you MIGHT need to have a film permit from the city of Santa Cruz to keep things legal.
I get the impression that State Park Rangers LOVE to give out citations...