Roll layers on terrace doors

That's the plan of the OP

And if you leave a small threshold and work with a slope? Should you still use a channel? Our roof overhang is about 50cm.

Wooden terrace up to the door (without a rolling layer). Then you also don't have an (unsightly) grate in front of it.

I personally also find that nice. I had already fixed on slabs quite firmly. I will take another look in that direction.

And what if you leave a small threshold and work with a slope? Should you still use a channel? Our roof overhang is about 50cm.

It always depends somewhat on the overall situation. With our neighbor, for example, the lawn, terrace, and floor are all at the same level. Paved terrace and door are flush with the ground. The terrace is also slightly lower than the street. In the past 2 years, there were 2 heavy rains where water stood 10cm high on the terrace and flowed into the living room—not just a little. That is probably an extreme situation. If the terrace is above the lawn and the slope generally goes away from the house with a 50 cm roof overhang, that should actually not be a problem.

because we specifically chose a low-profile design for the patio door. This was intended to avoid a higher threshold, but with the roller layer, there would be one again. On the internet, you find - as probably everywhere - divided opinions.

Divided pro or contra roller layer perhaps, but hardly divided on the question of construction height: with the roller layer it would already be about 12.5 cm due to the stone format, and effectively probably hardly under 14 cm because of the inclined installation - with the desire for a low threshold and/or even flush floor between inside and outside, I see this as only complicated to reconcile.

We also decided against a screed layer, which was also a good decision. Our terrace door is not directly level with the floor, it's just the "window frame" that you have to step over. The terrace itself is paved and has a slope towards the lower-lying garden... The roof overhang is 50cm but that doesn’t matter much with 2 full floors. Our garden landscaper said there are no problems.... Meanwhile, we already have a fixed terrace roof over it.