do Asana subtasks belong to projects?
Not yet
why?

Context

When subtasks were first introduced in Asana, they did not belong to their parent task's project. It was an initial design decision. Since then, based on community's feedbacks, Asana made several steps towards a situation where subtasks would fully belong to projects.
We know there are concrete features on both small term and long term roadmap, for example subtasks on timeline.

Solutions

Use sections and custom fields to limit the use of subtasks because often the parent task is a topic/category, not a real task.
Split a project into multiple projects to be more comfortable.

Learn

How to use subtasks
📖 The tale of Jerod the unwise in the subtask maze from Bastien
📖 (Learn to) Use Subtasks! from Larry

Join

The community and upvote product requests
🗳 Subtasks should count in Workload
🗳 Subtasks should show up in Calendar
🗳 Shift Task pane to the left to show Subtask details pane on right
🗳 Convert a subtask into a task
🗳 Visualise progress of subtasks
🗳 Connect subtasks' due dates with their parent task
🗳 Complete subtasks when parent task is completed
...

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from experts
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