Terrace connection terrace door

We are currently working on our terrace, now the question is how to design the connection to the terrace door. In the picture, you can see the current state....

Should insulation still be added here, if yes where and how much?

We simply went under the aluminum edge with our terrace slabs. One could have put a grid in front to keep water out. However, my parents didn’t do that either, and there have been no problems in 20 years. Visually, I don’t find those parts very appealing, so we left it out. Haven’t had any problems with it so far. The roof overhang is about 50 cm. The slope was 1.5%-2%. In my opinion, insulation is not necessary.