Do tasks assigned to me appear in my Microsoft To Do task list or my Outlook Task list?
Microsoft To Do
Tasks assigned to you in plan appear in Microsoft To Do under the Assigned to me option.
Microsoft Outlook
By default, tasks assigned in a plan do not appear in the Outlook task list.
You can get around this limitation using a Power Automate template called Create a task in Outlook Tasks when a Planner task is assigned to me. Note that the template only creates a task, it doesn't update it over time or register when it is completed.