Thank you for the many suggestions.
There is a lot to try now, unfortunately I have no experience with SubD.
It would be nice if you could simply apply SubD based on an existing surface.
Anything else should be difficult.
The Pillow script with loft is great, but has no solution for the round corners.
Michael's approach with sweep 1002.12 is interesting, but not easy.
If necessary, then bring the flat body with flow to the curved shape.....

I will report if there is a better result in sight than my previous one.