1. A cloud-connector subsystem comprising: cloud-connector nodes, each associated with a cloud-computing facility; and a cloud-director server that includes one or more processors, one or more memories, one or more data-storage devices, and computer instructions that, when executed on the one or more processors, control the cloud-director server to provide, in cooperation with the cloud-connector nodes: a management user interface that provides native management services and functionalities for creating, administering, and managing virtual data centers within one or more cloud-computing facilities, each associated with a cloud-connector node; an API entrypoint request/response interface to native services, a service-extension interface, service extensions created through the service-extension interface, and an authorization-service-management-interface; and an authorization service that controls access to service extensions created through the service-extension interface.