I can confirm this issue persists. I'm using the Outlook (PWA) with the sidebar "My Day" opened on tabpage "To Do". I've chosen "Planned" as the list to show.
There's a task assigned to me in a Planner plan with start- and due date. It does not show in the sidebar. When I just open To Do using the menu on the left in Outlook (PWA) and choose for the list "Planned", it does show that same task that's been assigned to me.
When creating a task directly in To Do for that same period (start and due date), that does show up in the sidebar panel where it should be. But as tasks are being assigned to me from different planner plans in our tenant it should pick that up in the sidebar no matter what.