gapic: REGAPIC invocation mechanics should be streamlined

The request setup for REST clients needs to be streamlined and simplified. The existing code was OK to start, but the request construction logic should probably be abstracted into `gax-go`. [Example](https://github.com/googleapis/google-cloud-go/blob/f60bde45662a74b55fd58305891a7fa4e44e4bdd/alloydb/apiv1/alloydb_admin_client.go#L2042-L2094).