Hi @AlexeiSo ,
Please kindly understand here we mainly discuss general issues on Outlook desktop client, we may know little about the detailed working priciple and integration between Outlook and Onenote. I have researched a lot about it but still in vain.
However, based on my research, for your requirement of accessing to the information of Outlook tasks from your product, I found some development articles that mentioned how access and manage outlook add-ins via script, for your reference:
Working with Outlook tasks: how to create, get and delete Task and To-Do items
(Please Note: Since the web site is not hosted by Microsoft, the link may change without notice. Microsoft does not guarantee the accuracy of this information.)
Hope that would be helpful to you. If you still need more help about script or development, it's recommended to add some development tag under your post.
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