I have seen that Outlook has a quick access toolbar (QAT).
You can access it doing below:
And then the QAT appears (see below screenshot, I marked it with a blue rectangle):
So taken into account that a custom task pane (ctp) have some limitations, for example, you cannot remove title bar nor buttons I was thinking about if it is possible to create a QAT programmatically and embed into it an WPF user control.
Is it possible?
No, it is not possible. At least there is no trivial way of getting the job done without Windows API functions involved.
The QAT (Quick Access Toolbar) has a predefined set of controls that can be put inside it. Read more about the Fluent UI (aka Ribbon UI) in the following series of articles: