This quite likely is half bug report, half feature request.
I was quite certain at some point I was able to construct a search using URL parameters, and in looking at the code in PhabricatorProjectSearchField.php that looked like a thing that was supported. However, if you attempt to use this feature it triggers an error when it attempts to setup the Viewer (->setViewer($this->requireViewer())) because $this->requireViewer() is not a defined method.
I'm not entirely sure how to connect the viewer in the best way. If you want to give some guidance, I'm happy to submit a fix here, too.