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I tried lots of test and research about the features you mentioned above, however, as of now, I'm afraid that there is no existed option in Outlook which could help us achieve those features. The interactions between Outlook and OneNote are very limited for now, you could only got the features as this document says: Send emails and meetings from Outlook to OneNote.
If you have a demand to add these functions to Outlook for Windows, you could create a thread in Outlook User voice, then other users will could vote on it for you, Microsoft may notice it and add it in the later version. Thanks for your understanding!
In addition, considering that you were trying to manage your mailbox items, Outlook Auto Archive feature could better help automatically archive your mailbox items and reduce mailbox size, for more information: Archive older items automatically.
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