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/index.md

@@ -9,7 +9,7 @@ When you need a quick HTTP server or client in C++, you want something that just
 
 The API uses a lambda-based design that feels natural. It runs anywhere you have a C++11 or later compiler. Windows, macOS, Linux — use whatever environment you already have.
 
-HTTPS works too. Just link OpenSSL or mbedTLS, and both server and client gain TLS support. Content-Encoding (gzip, Brotli, etc.), file uploads, and other features you actually need in real-world development are all included. WebSocket is also supported.
+HTTPS works too. Just link OpenSSL, Mbed TLS, or wolfSSL, and both server and client gain TLS support. Content-Encoding (gzip, Brotli, etc.), file uploads, and other features you actually need in real-world development are all included. WebSocket is also supported.
 
 Under the hood, it uses blocking I/O with a thread pool. It's not built for handling massive numbers of simultaneous connections. But for API servers, embedded HTTP in tools, mock servers for testing, and many other use cases, it delivers solid performance.