fix: address review comments on stdio subpath PR

- README.md: split root-barrel StdioServerTransport import into /stdio subpath
- packages/server/package.json: drop unused @types/cross-spawn devDependency
- CLAUDE.md: document runtime-neutral root barrel rule under Public API Exports

Author: felixweinberger

CLAUDE.md

@@ -74,6 +74,7 @@ When modifying exports:
 - Use explicit named exports, not `export *`, in package `index.ts` files and `core/public`.
 - Adding a symbol to a package `index.ts` makes it public API — do so intentionally.
 - Internal helpers should stay in the core internal barrel and not be added to `core/public` or package index files.
+- The package root entry must stay runtime-neutral so browser and Cloudflare Workers bundlers can consume it. Exports whose module graph transitively touches unpolyfillable Node builtins (`node:child_process`, `node:net`, `cross-spawn`, etc.) must live at a named subpath export (e.g. `./stdio`) and be covered by a `barrelClean` test in that package.
 
 ### Transport System
 

README.md

@@ -95,7 +95,8 @@ npm install @modelcontextprotocol/hono hono
 Here is what an MCP server looks like. This minimal example exposes a single `greet` tool over stdio:
 
 ```typescript
-import { McpServer, StdioServerTransport } from '@modelcontextprotocol/server';
+import { McpServer } from '@modelcontextprotocol/server';
+import { StdioServerTransport } from '@modelcontextprotocol/server/stdio';
 import * as z from 'zod/v4';
 
 const server = new McpServer({ name: 'greeting-server', version: '1.0.0' });

packages/server/package.json

@@ -92,7 +92,6 @@
         "@modelcontextprotocol/test-helpers": "workspace:^",
         "@modelcontextprotocol/tsconfig": "workspace:^",
         "@modelcontextprotocol/vitest-config": "workspace:^",
-        "@types/cross-spawn": "catalog:devTools",
         "@types/eventsource": "catalog:devTools",
         "@typescript/native-preview": "catalog:devTools",
         "eslint": "catalog:devTools",