We just changed a complete flat roof light as the unit had smashed. Most of these flat roofs can’t be reglazed. See if your insurance company will change it.
Don't think there is any beading or glazing cassette on that door. Open the door and look on top and see if there is a piece of wood you remove. If so the glass will slide out the top but you will need to take the door off the hinges to do this.
We fit solidor and a few years ago had no issues. They then got bought by the same company that owns doorstop. Now they seem to bow and crack. We are just about to fit our first hallmark door as an alternative.
2 things i would look at. Maybe the bay roof assuming that is a roof on top of the bay and also the rain running between the cill and bottom of the window and running back