Summary: Stand-alone application or extension of Calendar that has task cards that contain basic information - similar to Jira tickets.
Single task card should contain ID, summary, description, user defined labels, status (e.g. To-Do, In-Progress, Done), due date, etc. And preferably user definable fields.

Purpose of the app is to have a personal backlog of tasks, Kanban view and daily, weekly and monthly breakdowns of tasks with user definable filters.
Main benefit being integration of tasks with Mail, Calendar and Drive enabling users to link other items, making it a functional software ecosystem.

Bonus points for linked Gantt charts, and other project management functionality.