After a lot of trail & error I have now got the displays very close together. Perhaps my tips will help some of you and save you some unnecessary time wasting.
1) Nothing needs to be adjusted in Lightroom. No ICM, nothing.
2) On the iPhone I have only switched off "Night Shift" and "True Tone" and set the brightness slider Fix to approx. 2/3.
3) With the Software Viewsonic Colorbration it is now getting exciting. After many attempts and some Research, the following settings have emerged, how you should do the calibration (in my Case with a Datacolor Spyder x):
According to my information (Link), the iPhone 14 display Seems to not have an RGB-gamma but a gamma value of 2.22 (it looks like the black values go lower than RGB). And with some testing I was able to find out that a luminance of 200 cd/m² is closest to the iPhone's value.
After calibrating with the above values, I'm really happy. I can now edit the images in Lightroom as they will actually look on the iPhone.
Of course I don't know what settings the users out there have in the field, but at least in my home environment it works so well.
If I want to see approximately how it will look for users on a regular computer, I have saved a pure RGB calibration with 120 cd/m² and RGB-GAMMA on CAL2. This allows me to switch back and forth quickly.
And the same for print soft proofs, only with 80 CD/m² at CAL3.
Hope it helps someone.
Happy photography.