Here's a thought: On the "Extra files and folders" page, place a button that will "Scan for unusual profile files and folders" and anything found will be added to the "Additional Folders" tree or "Additional Files" list on this page and automatically checked. From there on the backup and restore is handled by existing code. You're work is done! Minimal changes to the gui, no change to the "just do it" use case, re-use existing code. Everyone wins!
This was essentially my suggestion in this thread two weeks ago:
the Extra Files & Folders tab could highlight them somehow. And a checkbox at the bottom 'Select All Non-Windows Folders' (which could also be controlled by the settings profiles feature).
My idea was to use the Extra Files & Folders feature that already exists, perhaps the 'unusual' folders could be highlighted in bold or a colour (if possible), but the main point being a simple option to 'select all non-windows folders' or words to that effect. When ticked it would select all the unusual folders in the existing Extra Files tree, then the files are backed up as per existing Extra Files code.
The only extra GUI element is the 'select all non-windows files' checkbox, and perhaps the highlighting of those extra files in the tree but this isn't essential. The simplicity of this implementation is the reason why I've been encouraging the useful new feature.
To my mind the only bit of this I'm unsure of is when there are multiple user profiles selected in the first step. Maybe the 'unusual' user profile files/folders should be selected only if they're in the user profiles selected to backup.
Don't forget, everybody: there is already a Windows 10 library folder in the profile folder that is ignored by the backup because it's new (3D Objects). I see this new development to the backup as a 'catchall' so new library folders don't necessarily need to be specifically added into code immediately. If the new library folder ends up being used it could be added to the GUI and code later.