I have the same problem. I'm on a MacBook Pro from 2012 and i'm running macOS Catalina 10.15.7, the highest it can run. May 9th, 2025 was the last day that OneNote did a backup of notebooks (which i had set to weekly, i believe). I believe it was a couple of days later that i noticed that i was getting a Sync Error and NOTHING was resolving it. I even uninstalled OneNote at one point. When i went to reinstall, that's when i realized the latest version did not work and then i went down a rabbit hole looking for a version of OneNote that was compatible.
Note: I run OneNote on my iPhone, my iPad, and my MacMini, and none of those were having issues. I could and still can even open OneNote on the web without issue. It's only on the MacBook Pro running macOS Catalina that has the sync error.
That said, i didn't have time to troubleshoot more until today (May 28th, 2025), when i finally identified the older versions that would install without issue. I was able to install version 16.66.1 (22101101), which i got from this website. However, i still get the Sync Error (0xE000006C cig68). I tried closing and opening the notebook, signing out and then back in. I even tried suggestions from this microsoft community website to no avail.
This particular onenote website says that version 16.77 addresses the issue, but 16.77 is not compatible with macOS Catalina (10.15). The weird thing is that it says the release date was 2022.10.12, but that is strange because that is the release date for version 16.66.1 (22101101), the version that is still installable on MacOS Catalina (which i mentioned before that i have installed).
It also might be useful to note that i had previously uninstalled OneDrive as well, and when i went to try to reinstall, it took me a while to find a version that still functioned for macOS Catalina, but i eventually found one, version 23.081.0416.0001 (Standalone). I had already installed this version and it was functioning and syncing appropriately before i even attempted to install and troubleshoot with OneNote. If OneNote relies on OneDrive for anything, i don't know what could be going wrong. I have plenty of drive space on OneNote if that's a concern.
I'm at my wits end, and i would love to know how to fix this. It looks like this happened all of a sudden to others like me (as seen from this thread). Microsoft must have done something to stop these old versions from syncing properly. Someone from Microsoft, please help.