Ref T12819. I started trying to get individual engines to drive these constraints (e.g., ManiphestTaskQuery can do most of the work) but this is a big pain, especially since most engines don't support "any owner" or "no owner", and not everything has an owner, and so on and so on. Going down this path would have meant a huge pile of stub functions everywhere, I think.
Instead, drive these through the main engine using the fulltext document table, which already has everything we need to apply these constraints in a uniform way.
Also tweak some parts of query construction and result ordering.