Two-way linking Projects property for tasks

The automatic context for tasks is a nice feature, but there should be an easier way of linking tasks with projects. If I want to manually add project as the task context, I need to search through all the possible objects of different types in the dropdown, which is clunky. I'd like to be able to search through Projects only (or ideally any other object type of choice, as it's possible for all the other objects).

It should also be possible to embed an Object query showing tasks based on Context (or based on the kind of property I mentioned above, such as Project), as it's possible for the other Object types.