Windows 10 Enterprise 64-bit, version 1909, having this problem since the notification was changed over to toast. My outlook is M365 MSO 16.0.13001.20266 32 bit. Clicking the notification doesn't open the email, just makes the notification go away.
On reddit there is a thread for this, by a microsoft agent I was asked to provide info on whether outlook was running elevated and whether a registry key was present:
First, determine if Outlook is running elevated. Right click on the Windows task bar and select Task Manager. Once opened, click the details tab, then right click on the
column headers and choose Select columns. Check the box for the Elevated column, and click OK. Scroll down to Outlook.exe, and look for Yes or No in the Elevated column.
Elevated = No
Second, you should have a registry entry that connects the Windows Action Center and Outlook. Open RegEdit (Open the start menu, then type regedit to search for it, open it.) Navigate to:
Computer\HKEY_CLASSES_ROOT\AppUserModelId\Microsoft.Office.OUTLOOK.EXE.15
or
Computer\HKEY_CLASSES_ROOT\AppUserModelId\Microsoft.Office.OUTLOOK.EXE.16
You should have one or the other of those above. Under that key you should have an entry called CustomActivator with the value {0006F0C6-0000-0000-C000-000000000046}
Computer\HKEY_CLASSES_ROOT\AppUserModelId\Microsoft.Office.OUTLOOK.EXE.15
CustomActivator = {0006F0C6-0000-0000-C000-000000000046}