So, the Gem for OneNote released in October 2019, adds the "Open Online Notebook" feature to help OneNote 2013, OneNote 2010 users open notebooks under Microsoft Work and School Accounts.
In Gem for OneNote -> “Gem” tab -> “Open Notebooks” menu -> “Open Online Notebook” menu item.
Gem will pop up a login window, input your Microsoft Work or School account and password to login.
Gem will list all notebooks of your account.
Double click on a notebook to open the notebook.
In this time, OneNote will pop up a login window.
Input the Work or School account and password again.
That way, OneNote can open a notebook of this Work or School account.
Then the notes will sync from OneDrive for Business.