Thank you very much! It seems that the (or at least one) reason for my issue was the step up booster on the sensor node.
This post gave me the hint, that the step up booster might produce noise:
https://forum.mysensors.org/topic/4796/battery-powered-sensors/67?_=1606408518798
So, now I power the nrf24l01 directly from the batteries and not through the step up booster anymore. Now the node is able to connect. There are still errors in the communication but not so many.
@BearWithBeard Wow, thanks for this detailed answer!
Today, I received an answer from Ebyte:
Yes, because of the shortage of chips, E01-ML01D is temporarily out of stock. It will be available in next mouth, if you have a purchase plan, please book as soon as possible.
@skywatch So, there is hope 
Sorry. Forget it. It was just some misunderstanding in the mycontroller UI.
I just saw that my sensors were in state "NEW" in mycontroller. I had to put it into state "REGISTERED". Don't ask me, why I thought that it worked via USB — I now think, that it never really worked, maybe i read the wrong line and saw another sensor in the list.
Wow! Thank you for your quick answer! That already helped a little bit.
At least I now saw, that the connection works, when my sensor node is powered via USB. So it seems to be a power issue on the sensor node. I'll dig deeper on this side.
Many thanks for your answers! I tried that thing with the sodium chloride solution and the values of my HYT221 sensor was far off (66%) whereas the measured values from the SI7021 showed 76%.
So I now configured an offset in MyController for the HYT221 sensors.
Thanks for your hints!