So, the technician is here and has now spent around an hour already replacing
the defective touchpad.

50% fixed! Left click works, Right click does not.

Second replacement scheduled.

Replacement part is delayed. Seems this happens so often, that they ran out of
touchpads.

DELL keeps me updating every two days, that there is no progress. Still waiting
for the replacement.

ETA for the part is now 2022-10-29. It's unclear however, where the part will be
at that time.

So, today a DELL service partner replaced the touch pad a second time. And it
still didn't work. The technician also couldn't make it work at first (like the
technician two weeks ago). However as they were sliding closer to the edge, it
suddenly started to work!

It seems that the newer touch pad models for the XPS 13 Plus massively narrowed
down the right click area. So I investigated. Here is a video recording, that
shows how ridiculously small the are is.
https://www.youtube.com/watch?v=R9BQgI6PWNw

In pictures:

The best part is however ... while recording the video and lighting up the touch
pad properly, I noticed that the technician made a mistake when re-installing
the keyboard. The area around the enter key is now elevated around 1 mm and
touches the screen when closed.