This is still being worked upon. I hope to have more details in the next couple months.
Please know the team is actively working on this feature.
Planner tasks should be visible in Teams on a My Tasks button on the main navigation, and you should also see all your own tasks in the Outlook tasks list. Not just the calendar and not through an calendar link, but a deeper integration with Outlook Calendar and Tasks that is automated when turned on.
276 votesJonathan commented
My Tasks should be a main navigation button like Activity, Chat, Teams, Meetings, Calls, Files. Productivity/Collaboration software should easily and quickly show you what you need to get done to help the team.