How can I do it even if I switch off the xbox so that it remains active in the Wi-Fi (have a Fritz box 7560)
I think this is only possible if you have the Xbox in energy-saving mode and then the setting matches it.
And how to set 😅
You should be able to change that when starting and starting. But that is just the catchphrase and other setting options follow, where I unfortunately no longer quite know which one to choose, but it should actually catch your eye.
Check out the console settings. Under "Energy and Start" you stay online with "Fast Startup" and loads updates etc. In the background.
Thank you worked 😀