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-util/llm-app/test_book.sh

@@ -4,8 +4,9 @@ set -euo pipefail
 # =============================================================================
 # test_book.sh — LLM App Tutorial (Ch1–Ch5) E2E Test
 #
-# Code is extracted from the doc markdown files (<!-- test:full-code --> and
-# <!-- test:cmake --> markers), so tests always stay in sync with the docs.
+# Code is extracted from the ja doc markdown files (the code block after each
+# <summary data-file="..."> line; see extract_code.sh), so tests always stay
+# in sync with the docs.
 # =============================================================================
 
 SCRIPT_DIR="$(cd "$(dirname "$0")" && pwd)"