The problem is that server backup will only show a status of set up/configured after running a successful backup despite "webadmin get versions" properly showing the list of backups.
After installing KB4552940 as part of the Extended Security Update for Windows Server 2008 R2 the wbengine.exe in the system32 folder is updated. What happens due to this is that the Microsoft-Windows-Backup service is unable to log Event 4 "The backup operation has finished successfully" & Event 14 "The backup operation has completed" to the Eventlog. After creating an Event Trace Session what you will see for these events is "The description for Event ID 4 from source Microsoft-Windows-Backup cannot be found." below that also saying "the message resource is present but the message is not found in the string/message table".
The BlbEvents.dll & BlbEvents.dll.mui files the EventMessageFile uses are not updated as part of this update so it seems the newer version of wbengine.exe is unable to find the strings it's looking for within those files. Replacing the wbengine.exe dated 4/16/2020 that came with this update, with an older version of the wbengine.exe file dated 3/2/2011 restored this functionality and allowed the server to report backup events as expected.
Side note, start events and failure events are still logged so it seems it's only some event descriptions it's unable to find. This is reproducible by freshly installing Server 2008 R2, and running all windows updates on a machine eligible for Extended Security Updates.