feat: add beUI MCP server on Cloudflare Workers

[starc007]

What

Remote MCP server exposing the beUI registry so AI agents (Claude, Cursor, etc.) can discover and install components.

Live: https://mcp.beui.dev/mcp (deployed, verified end to end).

Architecture

• mcp/ — Cloudflare Worker using McpAgent (Streamable HTTP + SSE). The Durable Object backs MCP session lifecycle (session id, capabilities, SSE back-channel) — it stores no registry data.
• Reads the live beui.dev/r/* endpoints at runtime, edge-cached 300s, so new components appear with zero worker redeploy. Single source of truth = the existing registry.
• No auth (public registry).

Tools

tool	input	returns
list_components	category?	slug, name, category, description
search_components	query	best-matching components
get_component	slug	description, deps, all source files, install command
get_install_command	slug, packageManager?	shadcn CLI command per package manager

Notes

• Pinned @modelcontextprotocol/sdk to 1.23.0 to match the copy bundled in agents (avoids duplicate McpServer type clash).
• Added ai to satisfy the SDK's dynamic import("ai") (chat-agent path we don't use, but esbuild must resolve it).
• Excluded mcp/ from the Vercel/Next build (.vercelignore) and from the root tsconfig/biome so the worker's Cloudflare types don't leak into the main build.
• Uses bun (bun.lock).

Verification

• Local + live smoke test: initialize → tools/list (all 4) → tools/call returns correct registry data
• mcp/ typecheck + wrangler dry-run pass under bun
• Main repo bun run check (typecheck + lint + registry) green with mcp/ present

Deploy

cd mcp && bun install && bun run deploy

Already deployed (version 49b989c4); custom domain mcp.beui.dev provisioned.