Door sill hanging in air supported only by frame above

[austin]

I'm replacing the front door. Removing the old door frame revealed an unbelievably poor installation by the original contractor. See the photos for a good laugh. Naturally, there has been a lot of water infiltration over the years resulting in wood rot. Anyway, what's the best way to remedy this situation before installing the new door? Sister joist, insulation, membrane, flashing ...??