I found a solution which I do not understand.
Suspecting the widgets, I took off the homepage. After switching off, the error was gone.
Then, I took the home page on but commented all widgets at the home page off - just the title were on. It led to a empty home page with title. But: Same error!
Then I reverted the home page options from "element" to basic, changed in the main options the home page and the error disappeared. I took all widgets on home page step by step back and the error did not come back.
I have no idea why the way of linking the home page element at the navigation leads to this error. I have the setup running on the dev site without errors.
Now, after reverting and configuring as basic type, the error has gone.
I hope, you can explain to me what the cause might be.
For the time being, the problem seems to be solved.