Currently, the async search task is the task that will be running through the whole execution of an async search. While the submit async search task prints out the search as part of its description, async search task doesn't while it should.

With this commit we address that while also making sure that the description highlights that the task is originated from an async search.

Also, we streamline the way the description is printed out by SearchTask so that it does not get forgotten in the future.