@Riley_Grant, Subtasks aren’t intuitive and can use significant improvement. One issue is that Subtasks don’t automatically belong to a Project. Vote here for this to be changed.
However, with the exception that search will find Subtasks in a Project. I don’t understand how this works since Subtasks don’t belong to the Project, and you found a hole, by searching in a Project Section.
If you want the Subtasks to explicitly belong to a Project or more specifically to a Project Section, you have to go to the Subtasks and manually add them (Tab-P) to the Project Section. If you do this, your search will work the way you want it to.