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/verify-type-equiv.ts

@@ -35,7 +35,7 @@ const root = resolve(import.meta.dirname, '..')
  * added to a doc with NO manifest entry is still discovered here and reported as
  * an orphan, instead of being silently skipped.
  */
-const MARKDOWN_GLOBS = ['README.md', 'docs/**/*.md', 'packages/*/*.md', 'packages/*/*/*.md']
+const MARKDOWN_GLOBS = ['README.md', 'docs/**/*.md', 'packages/*/*.md', 'packages/*/*/*.md', 'website/zh-CN/**/*.md']
 
 /** One manifest entry: a documented type-equiv block and its source symbol. */
 interface ManifestEntry {