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/c15-compression.md

@@ -29,7 +29,7 @@ std::string big_payload = build_payload();
 auto res = cli.Post("/api/data", big_payload, "application/json");
 ```
 
-With `set_compress(true)`, the body of POST or PUT requests is compressed before sending. The encoding is the first one enabled in your build, in the order Brotli, gzip, Zstd. The server needs to handle compressed bodies too.
+With `set_compress(true)`, the body of POST, PUT, or PATCH requests is compressed before sending. The encoding is the first one enabled in your build, in the order Brotli, gzip, Zstd. The server needs to handle compressed bodies too.
 
 ## Decompress the response