Maybe I am missing something, but it seems the projects.json is not a part of 3scale REST API (or I simply don't know how to access it) and I can't find any info about it in 3scale REST API docs.
I am able to do e.g:

curl -X GET "https://3scale-admin.apps.tremes-6798.openshiftworkshop.com/admin/api/services.json?access_token=<my_admin_token>"

but I am getting "status: Forbidden" when trying to do:

curl -X GET "https://3scale-admin.apps.tremes-6798.openshiftworkshop.com/p/admin/service_discovery/projects.json?access_token=<my_admin_token>"

Maybe it's because of OAuth proxy presence on the OpenShift cluster? Don't know