docs: add unauthenticated docs MCP proxy at /docs/mcp

[philip]

Summary

Makes /docs/mcp a real MCP server endpoint (not just a discovery descriptor) by proxying requests to mcp.neon.tech/mcp?category=docs, which exposes list_docs_resources and get_doc_resource without requiring OAuth.

• GET — unchanged, returns the MCP Foundation server.json descriptor pointing to ?category=docs
• POST — new: proxies MCP protocol requests (initialize, tools/list, tools/call) to the unauthenticated docs endpoint
• Middleware fix — adds docs/mcp to the static prefix exclusions so the middleware doesn't intercept MCP protocol POSTs before they reach the route handler

Depends on neondatabase/mcp-server-neon#230 adding unauthenticated support for ?category=docs. The check script will show 1 failure until that PR merges to production.

Test plan

• node scripts/check-agent-endpoints.js http://localhost:3000 — 8/9 pass (POST 401 until MCP PR merges)
• After MCP PR merges: all 9 pass
• npx vitest run src/app/\(docs\)/docs/mcp/route.test.js — 8/8 pass

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Project	Deployment	Actions	Updated (UTC)
neon-next	Ready	Preview, Comment	May 5, 2026 3:04am