Hi DanielUR,
Welcome to Microsoft Community. We glad to assist you here.
I understand that you are facing with the issue that OneNote "Search Notebooks" field covers the title and you cannot move it anywhere else. To inspecting your issue, could you please provide me your screenshots of One Note's Display setting. Go to One Note > File > Options > Display. Please make sure no personal information is visible on the screenshot.
While waiting for further assistance, you can try these workarounds:
- Try change to Vertical Tab layout and change back to Horizonal Tab. To change view layout, Go to View > Tabs Layout > Vertical Tabs/Horizonal Tabs

- Try change your display scaling. In some situation, UI elements misalign due to scaling issues. Go to Start > Settings > Display > Scale

- Check for One Note update. In One Note, go to File > Account > Update Options > Update Now.

- Try uninstalling and re-install One Note. To do this, go to Start > Control Panel > Under Programs tab, Click Uninstall a program > Find One Note and uninstall.
I hope this will help. Thank you for your patience and understanding.
If you have other questions, feel free to ask. I will try my best to help you
Sincerely,
Nam-D - MSFT | Microsoft Community Support Specialist