1. A system, comprising: a provider network comprising: a data center including a resource collection allocated for service requests received from a client network of a client, the client network distinct from the provider network; a plurality of endpoint routers linked to the data center by one or more private network paths, wherein access from the client network to at least a subset of the endpoint routers is configurable via a plurality of connectivity providers; and one or more computing devices configured to implement a connectivity coordinator; wherein the connectivity coordinator is configured to: implement an interface defining connectivity operations available to the client; receive a connectivity request from the client for dedicated connectivity to the resource collection from the client network, wherein the connectivity request is formatted in accordance with the interface; in response to the connectivity request, determine a particular connectivity provider of the plurality of connectivity providers to provide dedicated connectivity from the client network to a target endpoint router of the plurality of endpoint routers via a private or logically-isolated direct path, wherein the target endpoint router is configurable to provide a route over a private network path of the one or more private network paths in accordance with the connectivity request; generate a response to the connectivity request, wherein the response comprises an identification of the particular connectivity provider; and transmit the response to the client.