Wow, now I am honestly impressed...!
The vendor of the SIM7600E-H breakout board actually references V1.07 (https://www.ebay.de/itm/174664471081), which I cannot find anywhere to download in order to check if it is the same as 1.08 and from the vending page it cannot be downloaded. Contacted the vendor and asked for sending the referenced documentation already two times without response yet...
Previously I was working with V1.01, there it says the following and 2 does not even exist:

In the latest version I could find (https://www.waveshare.com/w/upload/8/8f/SIM7500_SIM7600_Series_AT_Command_Manual_V1.12.pdf), AT+CCHOPEN does not even exist. I was lost already - and it is not getting better...
I will continue trying to find the correct documentation and will also contact the beelogger specialists to check if what you found out above could be overcome somehow on their side.
Amazing help so far, thx a lot!
P.S. - Familiar with the copy and paste method - just makes messy posts, so I thought there is a better way like with integrating program code...
P.P.S: The new monitor output actually does seem to have something to do with using the BatteryShield directly instead of my external power supply unit...