I did a bit more research on this today. The banner message does seem to be a "timed nag" encouraging users to move all their documents to Onedrive.
The nag banner appeared for me in Excel again today. I started recording registry activity and then dismissed the banner. The following entry was updated:
[HKEY_CURRENT_USER\Software\Microsoft\Office\16.0\Common\KFM]
"KFMLastDismissTimestamp"=dword:655baf0b
That hex 655baf0b converts to today's date and the time I dismisssed the dialog. So, the time is being stored, presumably so that (after some period of time passes) the nag banner can be displayed again.
The "KFM" abbreviation refers to a OneDrive feature called "Known Folder Move" -- a simplified, one-step process that moves all user folders to OneDrive when activated. I found more information about KFM here:
Migrate Your Files to OneDrive Easily with Known Folder Move - Microsoft Community Hub
That information is targeted at businesses with domain-joined machines and provides an automated way, via group policies, to migrate user files to a "OneDrive for Business" account.
KFM is also used on personal (non-domain) machines and Onedrive Personal when a user chooses the OneDrive "backup" option, thus moving all the user's folders to OneDrive. There is no mention of the "nag" feature for KFM being built into Office, nor any mention of a way to block that banner. There is mention that if the group policy prohibiting users from redirecting user folders is set, then KFM will not work. But that may not prevent the nag banner from appearing within Office applications.
The answer MAY be this setting::
[HKLM\SOFTWARE\Policies\Microsoft\OneDrive]"KFMBlockOptIn"=dword:00000001
I have added that policy to my machine to test, but it will be a few days before I know if it worked (seems like the "delay" period between dismissing the dialog and it being shown again is around 2-3 days -- but I haven't tracked it so I am not sure of the precise period.)
If anyone else wants to test it, the documentation for that setting can be found here:
IT Admins - Use OneDrive policies to control sync settings - SharePoint in Microsoft 365 | Microsoft Learn