After being stuck (again, though not often enough to remember how I fixed it), my iPhone (and iPad) iOS devices stopped successfully synchronizing OneNote data.
Here's how I JUST fixed it, with effectively no risk to your saved data:
On my iPhone (noting OneNote on iPad iOS is different in many ways, and these steps are not tested this latest time on my iPad):
Open OneNote.
Click the "<" upper-left until you're all the way to the Notebooks screen, with your "accounts" aka "notebooks" listed. "More Notebooks" is listed as well.
Slide left on the notebook having sync. trouble, and select Close. You'll see a warning/confirmation. That explains you're not deleting anything - a big comfort compared to other steps I've seen on the internet!
Click More Notebooks, and follow the steps to add that problem notebook back into your list.
Done! Give it a minute to synchronize - be patient while everything is downloaded to your iPhone again. It took less than a minute for me, but a nervous minute until pages started becoming available.
My recent changes made on other devices now appear.
Some unorganized steps I've found online that didn't help:
Clicking away "... Sync Now" from within an open notebook page. I believe the same can be done by scrolling to the top, and pulldown. A "synchronizing circle" appears that way, no indication whether it did anything, but in my case it didn't.
iOS/Settings/Apps/OneNote/Reset OneNote/Delete Login Credentials (with OneNote not open btw) did cause the process to login again fresh to my Microsoft account, but did not help Sync. issues.
Force closing OneNote, restarting iPhone, and every other steps I could find on my iPhone and within OneNote did not help.
Updating the OneNote app, iOS updates, Etc. no help.