Apologize Jiaxing, yes they are two different examples. Please ignore the last one i posted. I'm creating a "test" task in the original task list (in the first site) where the workflow works to show you what is the
expected outcome:
As i assign a "test" task to myself "Zhang, Karen Jing Xin," a task was created automatically by the workflow down below the first line whereas in the first post, there was no task being created below the "test" task.

Clicking into the workflow, you will see the status shows "Stage 1" whereas in the first post, the status shows "completed"

For the problem demonstration on the subsite and setup on the subsite, please refer back to my first post. I think the real problem in the subsite is that the workflow completed without actually assigning the task. But the whole point of that "start a task
process" workflow is to assign tasks...could that be because the subsite does not have site admin permission or the "start a task process" workflow has discontinued?