If you want to waterproof your door you need to take out your door, completely cover your door with paint except the door knob, then apply 3 layer of polyurethane paint on the entire door except the door knob

This is the most cost effective but time consuming way of your don't want to change the door the polyurethane can provide hard film to resist scratches, and waterproof your door once it is cured even if it is a cheap door

you should have change to non-wooden door instead

what you can do now is to scrape and sand away the damaged part, then you use wood filler to make it look flat again, then paint and apply polyurethane to form a waterproof layer