website: wire the site into the repo gates; make every tutorial example compile

- website joins the pnpm workspace; root scripts website:dev/website:build;
  run-gates gains a website-build gate (ci-primary + ci-static) — the
  VitePress build doubles as the site's dead-link check; AGENTS.md documents
  the commands.
- doc-typecheck + verify-type-equiv now scan website/zh-CN/**/*.md; every
  ```typescript fence converted to ```ts and made standalone-compilable
  (55 compiled, 1 ignore-check). Phantom APIs the compiler caught are fixed:
  invented event names (agent/turn-end, tool/call, llm/pre-request, ready,
  dispose) replaced with real catalog events or per-plugin declare-module
  merges; presentCall/inject/Config claims corrected to the real shapes.
- guide/config.md entry-fields table completed against loader EntryOptions;
  its coding-agent example brought in line with examples/coding-agent.

package.json

@@ -9,7 +9,8 @@
   },
   "workspaces": [
     "vendor/*",
-    "packages/*/*"
+    "packages/*/*",
+    "website"
   ],
   "scripts": {
     "build": "tsc -b tsconfig.build.json && tsdown",
@@ -60,6 +61,8 @@
     "verify-persistence-catalog": "tsx scripts/gen-persistence-catalog.ts --check",
     "gen-module-graph": "tsx scripts/gen-module-graph.ts",
     "verify-module-graph": "tsx scripts/gen-module-graph.ts --check",
+    "website:dev": "pnpm --filter @deepseek-ai/website run dev",
+    "website:build": "pnpm --filter @deepseek-ai/website run build",
     "constraints": "tsx scripts/check-workspace-constraints.ts",
     "doc-sync": "pnpm run doc-typecheck && pnpm run verify-cordis-catalog && pnpm run verify-cordis-api && pnpm run verify-export-jsdoc && pnpm run verify-tool-catalog && pnpm run verify-config-catalog && pnpm run verify-persistence-catalog && pnpm run verify-doc-graphs && pnpm run verify-md-wrap && pnpm run verify-md-links && pnpm run verify-doc-refs && pnpm run verify-package-paths && pnpm run verify-mermaid && pnpm run verify-rfc-classification && pnpm run verify-rfc-format && pnpm run verify-type-equiv && pnpm run verify-translation-pairing && pnpm run verify-doc-budgets",
     "hygiene": "pnpm run knip && pnpm run publint && pnpm run constraints && pnpm run verify-node-next-types",
@@ -74,12 +77,14 @@
     "@agentclientprotocol/sdk": "0.25.1",
     "@stylistic/eslint-plugin": "^5.10.0",
     "@types/jsdom": "^28.0.3",
+    "@types/js-yaml": "^4.0.9",
     "@types/mdast": "^4.0.4",
     "@types/node": "^22.20.0",
     "@vitest/coverage-v8": "^4.1.8",
     "eslint": "^10.4.1",
     "fast-check": "^4.8.0",
     "jsdom": "29.1.1",
+    "js-yaml": "^4.1.0",
     "knip": "^6.16.1",
     "lefthook": "^2.1.9",
     "mdast-util-from-markdown": "^2.0.3",