cc, assuming you are able to do a crop rotation, grow something else that is not in the same group as peppers (includes potatoes, tomatoes, aubergines; "solanaceous" vegetable group) during the next year, at least. You may want to look up what those 2 wilts look like to see if you think you had V or F. There are some other plants that can get these wilts, so choose carefully.
There are many varieties in that group that are Fusarium wilt and Verticillium wilt resistant, especially tomatoes. Usually VF in the hybrid name, such as Celebrity (VFNTA). Next time you rotate back into solanaceous vegetables, seek out those varieties. Also, keep those dead peppers out of the compost pile (all my dead vegetable plants go to municipal composting since their system reaches higher temperature than my system).
You can also try solarizing that soil. Next season, when warm/hot, try spreading black plastic on the soil for a month. The high temperature should "cook" the fungus.
If it were my raised bed, I would try the above suggestions before discarding all that compost/soil, though that is an option. There are fungicides, but my preference is to avoid that route for vegetables. Others may have other opinions.
Best of luck to you!