docs(update): address review comments for MCP server guide (#41274)

* docs: improve BYOM guide for MCP server deployment and OAuth integration

* fix rebase

* fix pnpm.lock

* docs: clarify MCP guide and example naming

* fix pnpm-lock

* docs: remove basePath from MCP tutorial and example

- Remove misleading comment about Edge Functions routing
- Remove basePath as it's not needed - Edge Functions automatically strip /functions/v1/<functionName> prefix
- Simplify code to just use const app = new Hono()

* docs: clarify --no-verify-jwt flag and authentication options

- Explain that omitting --no-verify-jwt enables JWT verification at Edge Function layer
- Clarify this provides basic protection for internal servers but not full MCP auth
- Update authentication section to be consistent
- Add tip in deployment section about omitting the flag

* fiox format

* PR feedback

* chore: restore pnpm-lock.yaml from master

examples/edge-functions/supabase/functions/mcp/simple-mcp-server/deno.json

@@ -1,9 +1,8 @@
 {
   "imports": {
     "@hono/mcp": "npm:@hono/mcp@^0.1.1",
-    "@modelcontextprotocol/sdk": "npm:/@modelcontextprotocol/sdk@^1.17.3",
-    "@modelcontextprotocol/sdk/": "npm:/@modelcontextprotocol/sdk@^1.17.3/",
+    "@modelcontextprotocol/sdk": "npm:/@modelcontextprotocol/sdk@^1.24.3",
     "hono": "npm:hono@^4.9.2",
-    "zod": "npm:zod@^3.25.76"
+    "zod": "npm:zod@^4.1.13"
   }
 }

examples/edge-functions/supabase/functions/mcp/simple-mcp-server/index.ts

@@ -6,14 +6,13 @@ import { StreamableHTTPTransport } from "@hono/mcp";
 import { Hono } from "hono";
 import { z } from "zod";
 
-// Change this to your function name
-const functionName = "simple-mcp-server";
-const app = new Hono().basePath(`/${functionName}`);
+// Create Hono app
+const app = new Hono();
 
 // Create your MCP server
 const server = new McpServer({
-  name: "simple-mcp-server",
-  version: "1.0.0",
+  name: "mcp",
+  version: "0.1.0",
 });
 
 // Register a simple addition tool
@@ -25,8 +24,8 @@ server.registerTool("add", {
   content: [{ type: "text", text: String(a + b) }],
 }));
 
-// Handle MCP requests
-app.all("/mcp", async (c) => {
+// Handle MCP requests at the root path
+app.all("/", async (c) => {
   const transport = new StreamableHTTPTransport();
   await server.connect(transport);
   return transport.handleRequest(c);