docs: link the integration guide from both READMEs, fix three inaccuracies

Adds a pointer to docs/extending-codeman.md at the end of the API section in
README.md and README.zh-CN.md, so the guide is reachable from where people
read about endpoints rather than only from CLAUDE.md.

Reading the README's programmatic guide alongside the new page surfaced three
errors in it, all now fixed:

- POST /api/sessions/:id/input takes `useMux`, not `useScreen`. The latter is
  a legacy name that no longer appears in the schema.
- The page told integrators to send `\r` to submit. With `useMux: true` the
  server delivers text and Enter as two separate writes (writeViaMux does
  send-keys -l then send-keys Enter), so appending `\r` is wrong.
- "Unwrap the envelope" was incomplete: a few legacy GETs put the payload at
  the top level, so the advice is now `body.data ?? body`.

Also cross-references the README's programmatic guide, which covers the
in-session case (CODEMAN_MUX, CODEMAN_API_URL, CODEMAN_SESSION_ID,
CODEMAN_HOOK_SECRET_FILE) that the new page deliberately does not duplicate,
and documents the optional clientId/seq exactly-once fields.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

README.md

@@ -812,6 +812,8 @@ REST over Fastify — **~190 handlers across 20 route modules**, plus an SSE str
 | `POST` | `/api/clipboard`                | Push text to all connected browsers (`{text}`) |
 | `GET`  | `/api/sessions/:id/run-summary` | Timeline + stats                               |
 
+> **Building something on top of Codeman?** [`docs/extending-codeman.md`](docs/extending-codeman.md) is the integration guide: render your own UI as a tab, subscribe to the SSE event stream to react when an agent needs you, drive Codeman from a script, and the traps worth knowing before you start. Codeman has no plugin runtime on purpose, so an integration is just your own process talking HTTP.
+
 ---
 
 ## Architecture