I have deleted my rolling cache and now it seems to work. However, it does not use the configured copilot (in the identity configurator) but a random one.
I am not sure if the rolling cache deletion was the solution or that I entered a weight for pilot AND copilot (not only the copilot one). However, when I backed out of the flight and restarted another flight, I suddenly could only enter a weight for the copilot. Very strange. But in both cases I got a copilot, and in both cases a random one.
After another test, it was back to not showing the copilot, but during this test I entered the EFB (already in the aircraft sitting on the apron) and moved the slider for passenger weights to close to 100%, and suddenly 3 passengers appeared. I then was able to delete the passengers in the back row, and the one on the right seat was still there.
A note, maybe important: I noticed the copilot in the TBM (adhering to the configured copilot) does have a headset. The “copilot” in the DA40NG does NOT have a headset –> I assume that in the DA40NG, this is indeed not really a copilot but a random passenger. Under this assumption, it makes sense that the plane does not adhere to the copilot configuration. So as if the sim has planes where it thinks a real copilot makes sense and planes which it thinks are single piloted (what would be true for the DA40NG in most cases). Could that be?
The DA40TDI will not show a copilot/passenger at all. The funny thing is, the TDI does show the passenger weights in the weight circle (in the plane configurator). The DA40NG does NOT show the weights of the passengers – also strange.
I only tested the “Private Charter” versions – not sure what the difference to the default version is.
I retested the TBM and it still displays the copilot without any weight, and it is still the correct one, configured in the identity configurator.
TL;DR: The sim will now display a copilot in the DA40NG Private Charter (tested), but a random one.
The DA40TDI Private Charter (also tested) will not show a copilot, as already stated above by @DementedCorn327