A family of Microsoft products that enable users to capture, organize, and reuse notes electronically.
As far as I know, this issue appears to be similar to the repeated sign-in prompts in OneNote for Mac, iPhone, and iPad that Microsoft documented in the past for the OneNote 2016 version.
You can refer via: Fixes or workarounds for recent issues in OneNote for Mac, iPhone, and iPad
While this article relates to an older OneNote 2016 scenario and may not reflect the exact root cause of your current issue, it may still be worth trying the troubleshooting steps outlined there to see whether they help resolve your sign-in issue.
As a first step, please ensure that OneNote and all Microsoft Office applications on your device are fully up to date. If the issue persists after installing the latest updates, you could try clearing the Office credentials and signing in again so that new authentication credentials can be created on the device. This is one of the troubleshooting methods that Microsoft previously recommended for repeated sign-in and sync-related issues.
This could help ensure that your credentials stored on the device are properly synchronized with Microsoft's services and that any outdated, missing, corrupted, or expired authentication tokens are refreshed. Based on my research, OneNote may still appear to be signed in, while the token used for synchronization is no longer valid, which can result in repeated sign-in prompts and synchronization issues.
Regarding data safety, clearing Office credentials only removes your locally stored sign-in information from the device. It does not delete notebooks, remove data from OneDrive, or affect content that has already been synchronized to the cloud. After signing in again, OneNote will recreate the required credentials and re-establish its connection to the notebooks.
Note: As a precaution, I would recommend to verify that your notebooks are accessible from OneNote on the web or directly from OneDrive before performing any credential reset steps. This helps ensure that your notebook data is safely stored in the cloud before making authentication-related changes.
Additionally, since the issue appears to have started shortly after OneNote was configured on your iPad. As a test, you could try to sign out of OneNote on the affected iPad (or temporarily remove the account from that device) and then monitor whether notebook access and synchronization behave normally on your other devices.
If synchronization becomes stable after the iPad is disconnected, this could indicate that the issue is related to locally stored credentials, cached authentication data, or a device-specific synchronization issue on the iPad. Before signing out, however, please verify that any recent notes are already available in OneNote on the web to avoid the risk of leaving unsynchronized changes only on the device.
You could give this a try and let me know whether it helps. If you have any additional concerns or questions, please feel free to reply below. I would be more than happy to assist further.