Presently in BQ tasks project id is provided as part of JSON file. Once JSON file is validated, then it will be masked. As such it is not possible to know about the project id the task is associated in BQ.
Also, in our environment downstream applications uses project id as one of the key parameters to identify tasks for providing information about health of Tasks and other information associating with BQ project.
By having the projectid independently in GUI and through api, association of tasks and BQ project will easy, and helps other downstream applications.
Regards
RJ