I uninstalled OneDrive as soon as I could, so I haven't see the nag banners. But it really seems to be intrusive. This Microsoft Answer thread is two years old, 13 pages, and people are still adding "Me Too!"s. No solutions that seem reasonable and no mention of an option to disable.
Redirecting

>> I do not actually have it running in the background

That may not be completely true. It's set to autorun and may be there anyway. Do you know how to use autoruns to check?

Autoruns - Sysinternals | Microsoft Learn