Using New Outlook on Windows for professional communication and productivity
This seems to be working now. I tested opening existing file and making no changes, opening and updating - and in both desktop and web apps and they are all showing up almost immediately under Suggested Files (although only the last 3)....
But if you click on the option there that says OneDrive, you'll see all the Recent ones to choose from (even if they're stored in a Shared location, not your OneDrive)
Here is the version of Outlook I am on: