The list for "recently opened / closed files" shows an empty column, which looks like a column prepared for file icons - see image.

What is it really?
Will there be (file extension) icons? (Would be a fine thing.)

It can be seen on menu Datei (English: File) on same screenshot that every menu has the space for an icon. An icon is shown in this area of the menu if the menu item is associated with an internal command which is associated with an internal icon resource. Nothing is displayed in this area of the menu for other menu items like an internal command with no associated icon resource, or a submenu, or a menu item associated with a list entry (files list, windows list, projects list).

Is it possible to show also icons for list items?

Yes, in general it is possible on loading for a list item also an appropriate icon resource, manage the icon resource in memory together with the text shown in the menu, and associate the menu item icon resource with the icon resource of the associated list item. But that requires extra source code. The Microsoft libraries used to show lists in menus don't do that automatically.

Of course such a feature would slow down the application. In case of a files list shown in a menu it would be necessary to query with which icon resource a file displayed in menu is associated according to its file extension (stored in Windows registry). Then the file containing the icon resource must be opened which is most often an executable (EXE) or a dynamic linked library (DLL). This triggers the anti-virus application which scans the EXE or DLL file as being opened by an application (just for reading icon data, but the anti-virus application does not know that). Once the anti-virus application finished scanning the file for malicious code the application can load the icon resource into memory.

I have unchecked configuration setting Show registered file type icons in Explorer view in UltraEdit for the File View to much more quickly show the files lists although I am not often using this view. I have configured in my favorite file manager Total Commander to show the directories and files just with standard icons instead of the associated icons for the same reason.

However, if you would like to see the recently opened / closed files with their associated icons, you can request such an enhancement with an email to IDM support. I would suggest writing in email to associate this enhancement with the existing configuration setting Show registered file type icons in Explorer view so that users like me with no need for this enhancement do not suffer on reduced application speed, increased disk accesses and increased CPU usage for loading and showing icons for files listed in a menu.