@gerd_fuafsljfe, so I did another test run and did not touch the notebook while running.
My new results are:
I also logged the processor power and the temperature.
As seen here the power peaked when starting the benchmark, but while running the benchmark the CPU clearly seems to be limited to 15W:
The temperature was alway about 70°C (and also peaked while starting the Benchmark):
So there is still room for higher temperatures, but the power seems to be limited by software.
Remark: started logging while the first test was running.
You can see that the overall power and temperature was lower after the 6th test and this also explains why the results are worse after that. So I also think that this is software related. (wrong setting?)
Is there a solution to increase this limit only while the notebook is connected to a power supply?
Ok, that seems a lot better than I feared.
I dont really know how to disable the 15W limit because I did not have to. First I would check the BIOS, maybe there is something there.
Afterwards you will have to google around. This link looks promising: https://www.techpowerup.com/forums/threads/throttlestop-how-to-remove-throttle-flag.251139/
Somewhere on the internet you should be able to find how to do it on the 1065g7
As seen in the OP I modified the PSU of the Sapphire GearBox and swapped tha original fans to high quality ones. This mod works good so far.
Also the lagging problems are almost fixed now (see OP) and I can live with that.