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/ja/cookbook/w05-websocket-tls.md

@@ -26,6 +26,8 @@ if (ws.connect()) {
 
 証明書検証そのものを無効にしたい場合は`enable_server_certificate_verification(false)`が使えます。挙動の詳細は[T02. SSL証明書の検証を制御する](../t02-cert-verification)を参照してください。
 
+`WebSocketClient`には、独自の検証に使う`set_server_certificate_verifier()`と`set_session_verifier()`や、プロキシ用のセッター（`set_proxy()`、`set_proxy_basic_auth()`、`set_proxy_bearer_token_auth()`、`set_proxy_digest_auth()`、`set_no_proxy()`）もあります。CA証明書は最初の`connect()`で読み込まれるので、それより前に設定してください。
+
 ## クライアント証明書を使う（mTLS）
 
 `ws::WebSocketClient`には`PemMemory`構造体を受け取るコンストラクタがあり、`wss://`接続でクライアント証明書を提示できます。