Rewrite docs/client.md as a code-heavy, prose-light how-to guide

Restructure the document: action-oriented H1, Imports section,
section-opener concept links to the MCP overview docs (not the
specification), inline example-file references instead of `> [!NOTE]`
callouts, and a trailing "See also" section with cross-links plus an
"Additional examples" table.

New sections: Imports, Disconnecting (`terminateSession()` + `close()`),
Subscribing to resource changes
(`subscribeResource`/`unsubscribeResource`), Roots (`roots/list`
handler, `sendRootsListChanged()`), Error handling (tool errors vs
protocol errors, connection lifecycle callbacks, timeouts), and
`setLoggingLevel()` folded into Notifications.

All new code examples are type-checked regions in
`clientGuide.examples.ts` and synced via `pnpm sync:snippets`.

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: jonathanhefner

README.md

@@ -128,8 +128,8 @@ Next steps:
 
 - Local SDK docs:
     - [docs/server.md](docs/server.md) – building MCP servers, transports, tools/resources/prompts, sampling, elicitation, tasks, and deployment patterns.
-    - [docs/client.md](docs/client.md) – using the high-level client, transports, OAuth helpers, handling server‑initiated requests, and tasks.
-    - [docs/faq.md](docs/faq.md) – environment and troubleshooting FAQs (including Node.js Web Crypto support).
+    - [docs/client.md](docs/client.md) – building MCP clients: connecting, tools, resources, prompts, server-initiated requests, and error handling
+    - [docs/faq.md](docs/faq.md) – frequently asked questions and troubleshooting
 - External references:
     - [SDK API documentation](https://modelcontextprotocol.github.io/typescript-sdk/)
     - [Model Context Protocol documentation](https://modelcontextprotocol.io)