Yes, those are the two settings I have used (in Swedish of course).
I couldn't find anything about Profiles and Device Mgmg under Settings / Genereal.
But it is my private iPad, no organization or MDM software involved, to my knowledge.
I have removed OneDrive app, changed the settings like your picture again. turned the ipad off and on.
Then I started OneNote, and nothing happens, except that the icon on a white background is there. Microsoft at the bottom of the screen.
Then I double-clicked, and saw that OneNote was there. Clicked on it, and then after a few seconds, it is back (it seems) the the old behaviour.
It just blinks and disappears immediately.
Still hasn't been asked to login.
Double-click, and close: after that it starts and immediately disappears (active).
Installed Onedrive again: it seems ok (OneDrive, that is)
I clicked on one of the OneNote books in the OneDrive list: OneNote opens and closes immediately, as before.
Is there any more information I can collect to help solve this mystery?
.. / Jan