Until now I only have used Configuration::read and was happy.
I recognize now, if I use Configuration::write in the “public function initialize(): void” of a Controller, the value can be used within an action. But Configuration::write within an action seams not to work. I read the documentation but got no understanding. Thanks fpr clarfication!

Configure::write will work just fine anywhere, to add a value that is available for the remainder of the request. We’ll need to see some code and an explanation of what you’re trying to do in order to help resolve your issue.

I am also unable to reproduce this problem as you can see in the top screenshot

The Configure class is basically just a static class which holds data.
So no matter where you write to it the new data will be availalbe everywhere AFTER that Configure::write() call.