lint fixes and mermaid diagram updates

- alters the mermaid diagram to use http and not http/sse because sse is
  http and it allows it to be understood in a streamable http context
  too

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

Author: ChrisJBurns

docs/toolhive/guides-k8s/intro.md

@@ -36,23 +36,18 @@ The operator introduces a new Custom Resource Definition (CRD) called
 flowchart TB
   subgraph K8s["<h3>Kubernetes cluster</h3>"]
     subgraph K8s1["**Deployment**"]
-      Svc1["SSE Proxy<br>Service"] -- http/sse --> Proxy1["SSE Proxy<br>Pod"] -- stdio or http/sse --> MCP1["MCP Server<br>Pod"]
+      Svc1["HTTP Proxy<br>Service"] -- http --> Proxy1["HTTP Proxy<br>Pod"] -- stdio or http --> MCP1["MCP Server<br>Pod"]
       Proxy1 -.->|creates| MCP1
     end
     subgraph K8s2["**Deployment**"]
-      Svc2["SSE Proxy<br>Service"] -- http/sse --> Proxy2["SSE Proxy<br>Pod"] -- stdio or http/sse --> MCP2["MCP Server<br>Pod"]
+      Svc2["HTTP Proxy<br>Service"] -- http --> Proxy2["HTTP Proxy<br>Pod"] -- stdio or http --> MCP2["MCP Server<br>Pod"]
       Proxy2 -.->|creates| MCP2
     end
-    subgraph K8s3["**Deployment**"]
-      Svc3["StreamableHTTP Proxy<br>Service"] -- http/StreamableHTTP --> Proxy3["StreamableHTTP Proxy<br>Pod"] -- http/StreamableHTTP --> MCP3["MCP Server<br>Pod"]
-      Proxy3 -.->|creates| MCP3
-    end
-    Ingress["Ingress"] -- http/sse --> Svc1 & Svc2
-    Ingress["Ingress"] -- http/StreamableHTTP --> Svc3
-    Operator["ToolHive<br>Operator"] -.->|creates| K8s1 & K8s2 & K8s3
+    Ingress["Ingress"] -- http --> Svc1 & Svc2
+    Operator["ToolHive<br>Operator"] -.->|creates| K8s1 & K8s2
   end
 
-  Client["MCP Client<br>[ex: Copilot]"] -- http/sse or http/streamablehttp --> Ingress
+  Client["MCP Client<br>[ex: Copilot]"] -- http --> Ingress
 ```
 
 ## Installation

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

@@ -92,11 +92,11 @@ flowchart LR
   MCPService --> MCPPod
 ```
 
-### StreamableHTTP transport flow
+### Streamable HTTP 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.
+For MCP servers using Streamable HTTP 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
@@ -113,8 +113,8 @@ flowchart LR
     MCPPod["POD: MCP Server"]
   end
 
-  Client["Client"] -->|HTTP/StreamableHTTP| Proxy
-  Proxy -->|HTTP/StreamableHTTP| MCP
+  Client["Client"] -->|HTTP/Streamable HTTP| Proxy
+  Proxy -->|HTTP/Streamable HTTP| MCP
   MCPService --> MCPPod
 ```
 
@@ -180,7 +180,7 @@ When you apply an `MCPServer` resource, here's what happens:
 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 and
-   StreamableHTTP transport, a headless service is created for direct pod
+   Streamable HTTP 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