Notepad++ not automatically opening a tab for every file in its Backup folder.
The Backup folder sometimes has files that don’t correspond to any open tabs. So the Backup folder is not where the session is kept!
What you need is the actual session file. It is exported with File>Save Session..., and physically located at %AppData%\Notepad++\session.xml.
Edit: to easily get to this file, open any folder, and in the address bar at the top, paste in %AppData%\Notepad++. Or open that link with Run.
To get Notepad++ to use the session, this exact file needs to be synced. If OneDrive can’t do that, then you may have to symlink this file (or entire folder, even) with a place where OneDrive can put it.
You can learn how to symlink elsewhere on the internet; it essentially makes a shortcut, except fully live and not just a file that Windows Explorer can follow to open something else.