Hi Johannes,
I have noticed similar issues with my EOS RP C-RAW images. Reading the thread, I concur with Per's analysis.
The CR3 contains both the raw sensor data as well as the in-camera settings. DPP uses all this data whereas Lightroom accesses only the sensor data. I believe that LR can mimic some of the DPP behaviour using Camera Profiles although I haven't tried this myself.
If you want to retain the DPP processing in LR, one way is to export the image from DPP as a (16-bit) TIFF file and then import the TIFF.
My version of LR (6.14) doesn't support the CR3 format so I use the TIFF import method. This approach is preferable to using DNG Converter since the DNG file doesn't reflect the in-camera settings. BTW, the TIFF files are very large so I discard them after editing. If needed, they can be regenerated from the CR3 files using DPP.
Hope this helps.
- David