I think I’d need some more context of what page you’re trying to put the filter on.
(Image from SG’s User Guide)
The area on the right hand side is really just the Task Details page for each task you select on the left hand side. Within that, you can absolutely put a tab for Publishes and it will auto-filter for all publishes associated with that task.
Is that what you’re looking for? Or are you trying to see every publish from multiple tasks on a shot? If that’s the case, I don’t think the My Tasks area is the best choice for this, since you would have to be fighting against the context it’s presenting information in.