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/c13-max-timeout.md

@@ -4,7 +4,7 @@ order: 13
 status: "draft"
 ---
 
-The three timeouts from [C12. Set timeouts](../c12-timeouts) all apply to a single `send` or `recv` call. To cap the total time a request can take, use `set_max_timeout()`.
+The three timeouts from [C12. Set timeouts](../c12-timeouts) each cover only one step: the read and write timeouts apply to a single `recv` or `send` call, and the connection timeout to connecting. To cap the total time a request can take, use `set_max_timeout()`.
 
 ## Basic usage