There are two scripts in this thread which will solve the problem (a Batch file posted by me on 12/2/2023 and a Powershell equivalent posted by Denver Root on 12/5/2023). Both do the same thing, which is reset the "nag countdown date" to fool Office into believing the "nag" has been displayed and acknowledged today, so that it will not be displayed again.
The scripts need to be run daily via Task Scheduler. You need to copy/paste the script of your choice into a plain text file, with either a .bat or .ps1 suffix as appropriate for the script type you choose. Then create a Task Scheduler entry to automatically run the script daily. This will eliminate the Office "backup this document" banners from appearing.
The only other method that consistently works is to uninstall OneDrive. If you want access to OneDrive but do not want the periodic "backup this document" prompts, one of the scripts mentioned (with a Task Scheduler entry to run it daily) will eliminate the prompts.