Rot is common when the figs are on the tree too long. Pick when the individual fruit is soft and droops from the branch. Before they begin to drip.

Do you have swd in your area? The can ruin figs from the inside . https://m.youtube.com/watch?v=JHOQ45Wg0yQ

African fig fly is actually a much worse pest. SWD do sting unripe figs, but latex blocks the breathing tube and the egg dies before hatching. They can only survive in ripe figs, and are no worse than common vinegar flies according to what little research has been done.

https://journals.flvc.org/flaent/article/view/90767

Just because there are larvae in figs doesn't mean they are SWD, you need to put some figs in a jar (covered with fabric to breathe, and strips of paper towels inside for larvae to pupate on) and see what hatches out. AFF has 2 racing stripes and is slightly larger, I've never seen them turn interiors black though, they cause spoilage by way of introducing yeasts.

The only surefire way to prevent AFF is to cover the ostiole with a sticker or piece of tape once the figs begin to swell prior to ripening, but it is also important to bag all spoiled fruit and leave in the sun for the heat to kill them, though they will still come in from other areas.