Marking email as unread issue in Outlook app
Outlook's support team helped me.
They suggested to delete my account, subsequently clear the application's cache and then to add my account again.

Update: This seemed to work in the very beginning, but the issue actually persists.

Update2: The Outlook development team is investigating the matter. We'll have to wait for an update.

Update3: The issue is resolved since some time, presumably because Outlook fixed this bug and updated the app.