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/s20-keep-alive.md

@@ -52,6 +52,6 @@ Set `set_keep_alive_max_count(1)` and every request gets its own connection. Mos
 
 ## Relationship with the thread pool
 
-A Keep-Alive connection holds a worker thread for its entire lifetime. If `connections × concurrent requests` exceeds the thread pool size, new requests wait. For thread counts, see [S21. Configure the thread pool](../s21-thread-pool).
+A Keep-Alive connection holds a worker thread for its entire lifetime. The pool adds threads under load, up to its maximum thread count (4× the base count by default). If open connections outnumber that maximum, new connections wait in the queue until one closes. For thread counts, see [S21. Configure the thread pool](../s21-thread-pool).
 
 > **Note:** For the client side, see [C14. Understand connection reuse and Keep-Alive behavior](../c14-keep-alive). Even when the server closes the connection on timeout, the client reconnects automatically.