vMCP: Use proxy-mode instead of transport (#2413)

I got hit by this again... We should be using proxy mode when
determining the transport to use for an MCP, and not the MCPs underlying
transport which is not useful for this scenario.

Signed-off-by: Juan Antonio Osorio <ozz@stacklok.com>

Author: JAORMX

pkg/vmcp/aggregator/cli_discoverer.go

@@ -74,11 +74,20 @@ func (d *cliBackendDiscoverer) Discover(ctx context.Context, groupRef string) ([
 		healthStatus := mapWorkloadStatusToHealth(workload.Status)
 
 		// Convert core.Workload to vmcp.Backend
+		// Use ProxyMode instead of TransportType to reflect how ToolHive is exposing the workload.
+		// For stdio MCP servers, ToolHive proxies them via SSE or streamable-http.
+		// ProxyMode tells us which transport the vmcp client should use.
+		transportType := workload.ProxyMode
+		if transportType == "" {
+			// Fallback to TransportType if ProxyMode is not set (for direct transports)
+			transportType = workload.TransportType.String()
+		}
+
 		backend := vmcp.Backend{
 			ID:            name,
 			Name:          name,
 			BaseURL:       workload.URL,
-			TransportType: workload.TransportType.String(),
+			TransportType: transportType,
 			HealthStatus:  healthStatus,
 			Metadata:      make(map[string]string),
 		}