docs: adds streamablehttp docs for K8s

Signed-off-by: ChrisJBurns <[email protected]>

Author: ChrisJBurns

docs/toolhive/guides-k8s/run-mcp-k8s.md

@@ -92,6 +92,33 @@ flowchart LR
   MCPService --> MCPPod
 ```
 
+### StreamableHTTP transport flow
+
+For MCP servers using StreamableHTTP transport, the proxy creates both
+a pod and a headless service. This allows direct HTTP communication between
+the proxy and MCP server while maintaining network isolation and service
+discovery.
+
+```mermaid
+flowchart LR
+  subgraph Proxy["Created by Operator"]
+    direction TB
+    ProxyService["SVC: ToolHive-Proxy"]
+    ProxyPod["POD: ToolHive-Proxy"]
+    ProxyService --> ProxyPod
+  end
+
+  subgraph MCP["Created by Proxy"]
+    direction TB
+    MCPService["SVC: MCP-Headless"]
+    MCPPod["POD: MCP Server"]
+  end
+
+  Client["Client"] -->|HTTP/StreamableHTTP| Proxy
+  Proxy -->|HTTP/StreamableHTTP| MCP
+  MCPService --> MCPPod
+```
+
 ## Create an MCP server
 
 You can create `MCPServer` resources in namespaces based on how the operator was
@@ -117,7 +144,7 @@ metadata:
   namespace: my-namespace # Update with your namespace
 spec:
   image: ghcr.io/stackloklabs/osv-mcp/server
-  transport: sse
+  transport: streamable-http
   port: 8080
   permissionProfile:
     type: builtin
@@ -153,7 +180,7 @@ When you apply an `MCPServer` resource, here's what happens:
    service to handle client connections
 4. The proxy creates the actual `MCPServer` pod containing your specified
    container image
-5. For STDIO transport, the proxy attaches directly to the pod; for SSE
+5. For STDIO transport, the proxy attaches directly to the pod; for SSE and StreamableHTTP
    transport, a headless service is created for direct pod communication
 6. Clients can now connect through the service → proxy → MCP server chain to use
    the tools and resources (note: external clients will need an ingress
@@ -217,9 +244,8 @@ metadata:
   namespace: development # Can be any namespace
 spec:
   image: ghcr.io/stackloklabs/gofetch/server
-  transport: sse
+  transport: streamable-http
   port: 8080
-  targetPort: 8080
   permissionProfile:
     type: builtin
     name: network
@@ -474,7 +500,7 @@ Common causes include:
   selectors
 - **Port configuration**: Verify the `port` field matches the MCP server's
   listening port
-- **Transport mismatch**: Ensure the `transport` field (stdio/sse) matches the
+- **Transport mismatch**: Ensure the `transport` field (stdio/sse/streamable-http) matches the
   MCP server's capabilities
 - **Network policies**: Check if network policies are blocking communication