Have you found a solution to this question? Please let us know what you have tried and the status. What version of Tableau are you using as well?
I'm using Tableau 10.5. I've tried many times to put in the request some value that can produce parentProjectId=null, for example: "?filter=parentProjectId:eq:null","?filter=parentProjectId:eq:''", etc.
Currently, I'm simply filtering projects from the response on Java server-side, but I want to find a more efficient solution for this case, cause performance will be terrible in cases of huge Tableau project structures.