If I'm reading this report correctly[1], California's car registration fees and gas taxes cover more than the cost of roads. Caltrans estimates $20.2 billion in revenue from fuel taxes and vehicle registration fees, while their budget is $18.7 billion.
It also looks like public transportation is mostly paid for with sales taxes, federal loans/grants, and $1 billion of taxes on diesel fuel.
Note that Caltrans only maintains state roads; looks like from that document that they distribute some money to localities but as far as I can tell we can't see what fraction of local road maintenance that covers. Of course localities also have parking fees, traffic tickets, etc that can help cover road maintenance.
That's difficult to untangle due to multiple agencies. Local, State, and Federal. However, the answer is the overwhelming majority of road construction and maintenance is paid for by gas taxes, car registration, and tolls.
It also looks like public transportation is mostly paid for with sales taxes, federal loans/grants, and $1 billion of taxes on diesel fuel.
1. See chart A on page 24, and chart F on page 28: https://dot.ca.gov/-/media/dot-media/programs/budgets/docume...