Organization Read Only entitles you to effectively have Project Read Only for each Project. However Project Read Only is not the same as Project Data Access Read Only.
I do apologize that “Project Read Only” and “Project Data Access Read Only” are so similarly worded: this has a legacy reason that I won’t go into. Really “Project Read Only” should be called “Project Metadata View Only” since it does not grant access to cluster data contents.
-Andrew