Fix README and docs pages that no longer match the code

Bring the READMEs and the docs pages (en and ja) in line with the
current header:

- Fix the client sample that does not compile, the Transfer-Encoding
  statement for default headers, the verifier callback comment, the
  thread pool spawn rule, the sanitize_filename description, and the
  inverted Accept-Encoding sentence.
- Describe recent behaviour: TLS errors behind Read/Write failures,
  Host validation, Connection: close for a body without length,
  content_reader rules, refused CONNECT, WebSocketClient proxies,
  CPPHTTPLIB_INTERIM_RESPONSE_MAX_COUNT, the SSE event size limit, and
  the payload limit of the Stream API.
- Complete the API references of WebSocket, WebSocketClient and the
  stream:: helpers, and the SSE reconnect rules.
- Fix cookbook pages: keychain loading on every backend, received Close
  status, a multipart sample that trusted the client's file name, an
  echo sample that sent binary as text, SNI, pre-request handler scope,
  stop() with WebSocket handlers, and the thread pool notes.
- Restore the mutex in the LLM app's Chapter 5 code.

docs-src/pages/en/cookbook/c16-proxy.md

@@ -17,6 +17,8 @@ auto res = cli.Get("/users");
 
 The request goes through the proxy. For HTTPS, the client uses the CONNECT method to tunnel through — no extra setup required.
 
+If the proxy refuses the tunnel, the request fails with `Error::ProxyConnection`. The exception is a 407: it comes back as the response, so `res` is truthy and `res->status` is 407, while `res.error()` still returns `Error::ProxyConnection`.
+
 ## Proxy authentication
 
 If the proxy itself requires authentication, use `set_proxy_basic_auth()` or `set_proxy_bearer_token_auth()`.