I am very much a newbie gardener. I found out the hard way that I was definitely over watering my pepper seedlings, which led to root rot and leaves falling off, as well as the main stem (the tip of it) looking dry. I have recently transferred the plants into new soil, and although they look healthy, I have no idea if the main stem will repair itself and keep growing/producing leaves, or if the harm has been done and there is no chance for survival.
It is possible to save pepper seedlings from root rot if you catch it early on. Your plants were severely affected and most likely won't make it. I agree with @OrganicLawnDIY, start some new ones to stay on the safe side. If any of the diseased plants survive, they won't have the vigor of healthy seedlings. It is tricky to save plants from root rot, because once you can see the effects it is generally too late. I have saved an aloe vera from root rot, so I know it can be possible.