Thank you for this, I noticed that my OneNote notebooks in OneNote 2016 wouldn't show up if I wanted to open them after them being closed. I had a feeling by unchecking the "Enable connected experiences", which can be found under Account > Manage Settings (under Account Privacy) > All connected experiences, you also loose access to OneNote Notebooks saved in OneDrive.
I then rechecked "Enable connected experiences", opened OneNote 2016 and found the notebooks I couldn't find earlier but of course the yellow notification showed up again.
I then played around with the options under "Manage Settings", unchecked both:
1) "Experiences that analyze your content"
2) "Experiences that download online content"
to no avail. Unchecking both does not remove the yellow notification.
For now, the only solution to remove the yellow notification is the assigned "best solution" but it will remove OneNote 2016's access to your notebooks (which I use regularly).
If there are any other solutions that don't require to uncheck "Enable connected experiences", please let us know in this forum.
Thank you GuangP for your help!