I finally made my field customizer work in SharePoint online. It provides a URL field with modified link based on other item metadata.
It creates a custom view which shows the new column provided by the field costomizer.
It works fine on the main page of the library, but when I add a web part with the library to display it on a modern web page together with other stuff, the column stays empty.
Is it by design, is there a trick or is it a bug?