I finally found a solution to make the serial monitor work reliably to
copy all content
auto connect / disconnect
save to file
well making it work reliable is done by not using the inbuild serial but with using an extra terminal-software called HTerm make serial debuging work download HTerm
You can mark in the receive window and even go on receiving
It's well known that 3rd party terminal programs are superior to Serial Monitor; it also has been advised numerous times to use them to work around the limitations of the current Serial Monitor.
The only pitfall is that you have to disconnect the 3rd party terminal program before uploading new code via USB.
If you have found a way to automatically disconnect when an upload starts, please please please share