It does sound like fusarium wilt which is a pain. Basil plants in my experience like it on the dry side. I have one here in Michigan that is 3 years old. It almost died this last winter, lost most of it’s leaves, but is making a comeback. It is a hybrid that won’t die after flowering. Also they hate cold weather, if night temps are below 50F bring it in. Some bacteria in compost love eating fungus. I always mix compost in my potting soils. Numerous studies confirm this just google compost and damping off in Google scholar to see the studies. Several fungi can cause decay of seeds and seedlings including species of rhizoctonia, fusarium and phytophthora. However, species of the soil fungus pythium are most often the culprit for damping off. Compost works best here, but may help with fusarium too.