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.

scripts/doc-typecheck.ts

@@ -2,7 +2,8 @@
  * Doc-sync gate (doc-sync-enforcement RFC, part 1): typecheck the fenced `ts` code blocks in our
  * Markdown so documentation can't drift from the API it documents.
  *
- * Every ```ts block in README.md, docs/** and packages/* /README.md is
+ * Every ```ts block in README.md, docs/**, packages/* /README.md and the
+ * website tutorial pages (website/zh-CN/**) is
  * extracted to a temp typecheck project and compiled against the workspace
  * sources through the same project-reference boundaries used by repo
  * typecheck. A block that is a deliberate sketch rather than compilable code
@@ -134,7 +135,7 @@ function tempTsconfig(): string {
   })
 }
 
-const markdownGlobs = ['README.md', 'docs/**/*.md', 'packages/*/*.md', 'packages/*/*/*.md']
+const markdownGlobs = ['README.md', 'docs/**/*.md', 'packages/*/*.md', 'packages/*/*/*.md', 'website/zh-CN/**/*.md']
 
 const files: string[] = []
 for (const pattern of markdownGlobs) {