I find I can leave blueberries on the bush for a fairly long time. That may not be the case in warmer climates. This assumes bird protection, of course. Rhubarb would be another. And aronia.
Citrus such as navel oranges can hang for over a year.
Your best bet for high “hang time” as you define it is citrus of various kinds. Figs don’t qualify
Not sure if you can grow them in NorCal, but avocados have what feels like an endless hangtime. Mangos also have a pretty large harvest window.
You could also graft different varieties of figs that have different ripen times (or just get mutiple if you have the space). There is at least one variety of fig that ripens more or less each month, would just have to research and plan. You could also apply this same strategy with most fruit trees (multigrafts are very good for extending harvest seasons).