One reason for the sync issue is because OneNote uses different default locations for the Quick Notes section on different platforms.
The default Quick Notes in desktop creates and uses a notebook which is stored in
UserProfile/Documents/OneNote Notebooks. This notebook may not be synced to your Microsoft account and so can’t be viewed in the Android app. The default Quick Notes location for Android is usually under
username Notebook but if it doesn’t exist, the app chooses the first available notebook and creates a section under it called ‘Quick Notes’ and to use as the default location.
To fix this issue, pick the same default notebook and section for Quick Notes on the desktop, Android and iOS apps. To pick the default location:
Desktop app: File > Options > Save & Backup > Save > Quick Notes section > click the Modify button and select a section that is under the Microsoft account and synced. Default location is usually
C:\Users\username\Documents\OneNote Notebooks\My Notebook. Change this to a OneDrive location in the form of
Android app: Notebooks > Select a notebook > Select a section > press and hold the section > tap 3 dots menu > Set as default
iOS app: In the iOS app, you can’t select a section for Quick Notes. Instead you can only select a Notebook. Selecting a notebook then creates a new section in it called Quick Notes. Ensure that the settings in the Desktop & Android app have selected the same Quick Notes section as the one on iOS. The option for iOS is available under Settings > Quick Notes