Most older cities have what are called combined sewers (there is a good wikipedia article on it) and have to deal with this problem in various ways.
This is a common story around the world but Prop 13 adds the wrinkle that it mostly affects new buyers and people who haven’t figured out how to pass property to their descendants without resetting the tax assessment. That guy who bought a place in PB with his back pay when he got out of the Navy is still paying $100 a year in taxes. He has a massive incentive not to do anything which will reset that, so the city won’t be getting more revenue that way until he (or his heirs) sell the place.
IIRC, there are physical limitations on the city's ability to filter sewage and stormwater -- it all runs through the same pipes, and it would be a momentous undertaking to split the systems (some of those pipes are 200+ years old, and aren't accurately mapped). Wastewater treatment capacity is slowly increasing, however.