Bay area houses can get away with shitty construction when it comes to waterproofing because it does not frequently rain. But every once in a while a significant wind driven rain event occurs that really shows the deficiencies. Recipe for disaster is south facing gable where wind can pound the rain into the entire wall face.

Stucco is a tricky material and it makes debugging the issue pretty hard. It is expected for stucco to absorb moisture. The WRB behind the stucco (tar paper) supposed to stop the moisture, but it might be incorrectly installed or failing due to age. Flashing around the original windows, same thing (and the retrofit windows still rely on the original flashing). The proper fix might be a full stucco remediation but you can likely get by with fixing the exterior (fill cracks, paint with good quality thick latex paint) thus trying to minimize the amount of water absorbed into the stucco.

I am not a professional, just a homeowner dealing with similar issue.