For freight? It's pretty solid.
In calendar year 2019, the alameda corridor [1] processed about 4.8 million twenty foot equivilent units (TEU) [2] and the ports of los angeles and long beach processed about 9.3 million [3]. So around about half of the container trips to or from the port are by rail rather than truck. Some of the containers may just get put on trucks at the rail yards at the other end of the corridor to avoid trucking congestion in the port, but I don't think there's a lot of that. (I could be wrong)
For passengers? It's pretty iffy outside of commuter rail, Amtrak operates on freight lines, and is deprioritized, and there's a lot of freight volume, so there's a lot of delays for passengers.
I don't know the right keywords to find data for the ports of Oakland and Stockton. They probably have a decent rail volume too, but they have more challenging geography to get east than in southern california.
[1] the rails between the port of la/long beach and major rail yards exiting los angeles
[2] http://www.acta.org/pdf/Monthly_TEUREV_History.pdf
[3] https://kentico.portoflosangeles.org/getmedia/a43d3038-7713-...