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.

AGENTS.md

@@ -30,6 +30,7 @@ packages/    Harness packages at packages/<group>/<pkg>/, all named @deepseek-ai
 examples/    Runnable demos: thin cordis.yml leaves over the app packages (see examples/AGENTS.md)
 docs/        architecture, generated catalogs, RFCs, postmortems, cookbook (see docs/AGENTS.md)
 scripts/     repo gates and generators
+website/     VitePress docs site (zh-CN)
 ```
 
 Per-package map: the group READMEs, indexed from [packages/README.md](packages/README.md).
@@ -48,6 +49,7 @@ pnpm run lint
 pnpm run build          # tsc emits lib/types, tsdown bundles runtime
 pnpm run hygiene        # knip + publint + workspace constraints + NodeNext consumer check
 pnpm run doc-sync       # all documentation gates; see the doc-sync script in package.json
+pnpm run website:build  # VitePress build (doubles as the site's dead-link check)
 pnpm run demo:echo      # mock-model REPL, no key needed
 pnpm run demo:repl      # real REPL coding agent (needs DEEPSEEK_API_KEY)
 pnpm run demo:cordis    # self-referential demo: the agent modifies its own runtime (needs key)
@@ -65,6 +67,7 @@ pnpm run lint
 pnpm run test:coverage
 pnpm run test:snapshot
 pnpm run doc-sync
+pnpm run website:build
 pnpm run verify-module-graph
 pnpm run build
 pnpm run hygiene