Yup you're right that you can filter tasks with a category parameter (you can also specify multiple categories by comma-separating the IDs). We haven't documented this endpoint yet as it's an internal endpoint that might change in the future.
We are looking to extend the existing filtering/search endpoints in the future and this is definitely something we'll look at. Filtering users by status is something that we'll probably also look at as part of this. (btw the status parameter that you tried is ignored as there are no parameters for this endpoint. Nice try though!).
Thanks for the feedback,