The current SOAP API used to retrieve projects (getMyProjects @
https://tuleap.net/soap/wsdl) return the list of projects the user belongs to but not the list of projects that the user can see but in which the user does not belong (public projects). A new operation (getProjects?) or an improvement of the behavior of the existing one (getMyProjects) would be needed to retrieve all the projects that the user can interact with.