At Configuration - File Handling - Miscellaneous make sure that there is setting Close all files when opening or switching projects not checked.
Now create a new project/workspace with a name like OpenFiles for example in the directory of the INI of UEStudio/UltraEdit. Click on button +All Open Files and close/save the project.
Now you have what you want.
Whenever you need a function list or IntelliTips for all open files and the list of opened file has changed, re-open the OpenFiles project, remove all existing files and add all open files.
An automatical symbol database handling for open files without a project is not a really good idea because then UE or UES has to update always the symbol database when a file is closed or a new is opened. Think about the delay created when opening 200 files at the same time or opening a file with 100 MB and more because of the search for symbols. But even for closing/opening 1 small file the necessary update of the database would result in a loss of performance because I would have to wait for the finish of the symbol update process.
Sure, instead of an automatic database update a manual "create symbol database for all open files" could be implemented. But this would just save a few clicks in comparison to what I have suggested above. I think, most of us working with function lists for more files than the current file and IntelliTips simply work with projects and workspaces.
Is working with a project not also an option for you?