Superbinë to the rescue!

Apparently not everyone understood my description of the problem. I was describing the ideal situation where water would flow from all sides towards the drain. Otherwise there would need to be a lip on one side. But it turns out this is standard.

And it’s fine as long as everything is properly sealed. This is pretty straightforward as the following video (in German) explains.

Bodengleiche Dusche einbauen: Linienentwässerung | Anleitung von HORNBACH

Bodengleiche Dusche einbauen: Linienentwässerung mit der Anleitung von HORNBACH: Schritt für Schritt mit Material- & Werkzeugliste ✔ Jetzt i

Time permitting we should be okay.

We are so far out of our depth! So, thanks again to Binë for taking the time to explain these things and send the useful links!