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>

docs/extending-codeman.md

@@ -40,6 +40,17 @@ curl -u admin:$CODEMAN_PASSWORD http://127.0.0.1:3000/api/v1/sessions
 or `body.success`, then read `body.data`. The full `errorCode` to status mapping
 is in [`api-reference.md`](api-reference.md).
 
+⚠️ A few legacy GETs (`/api/away-digest` among them) return a bare-ish body with
+the payload at the top level rather than under `data`. Read defensively with
+`body.data ?? body`.
+
+**Already driving Codeman from an agent?** The README's
+[Programmatic Guide](../README.md#driving-codeman-from-an-agent--programmatic-guide)
+covers the in-session case: the `CODEMAN_MUX`, `CODEMAN_API_URL`,
+`CODEMAN_SESSION_ID` and `CODEMAN_HOOK_SECRET_FILE` variables that let a CLI
+running inside Codeman find the API and avoid acting on itself. This page is for
+code running *outside* a session.
+
 ## Seam 1: Web tabs
 
 The highest-leverage seam. Any web app you can serve locally becomes a tab beside
@@ -156,12 +167,17 @@ curl -u admin:$PASS -X POST http://127.0.0.1:3000/api/v1/sessions \
   -H 'Content-Type: application/json' \
   -d '{"workingDir":"/home/me/project","mode":"claude"}'
 
-# Send a prompt (single-line only, "\r" submits)
+# Send a prompt (single-line only)
 curl -u admin:$PASS -X POST http://127.0.0.1:3000/api/v1/sessions/$ID/input \
   -H 'Content-Type: application/json' \
-  -d '{"input":"run the tests","useScreen":true}'
+  -d '{"input":"run the tests","useMux":true}'
 ```
 
+`POST .../input` also accepts `clientId` (stable per client, max 128 chars) and
+`seq` (monotonic per session). Send both and the server applies each pair
+at-most-once, so retrying after a dropped connection cannot type the prompt
+twice. Omit them entirely rather than sending `null`.
+
 For shell scripting, the `codeman` CLI is the same surface without the HTTP
 plumbing:
 
@@ -205,8 +221,10 @@ Every one of these has cost somebody real time.
   shipped bugs more than once.
 - **`text/plain` bodies stay raw.** Auto-parsing them as JSON enabled
   simple-request CSRF, so it is deliberate. Send `application/json`.
-- **Prompts are single-line.** Input is delivered as text plus a separate Enter;
-  a multi-line string breaks the agent's input handling. Send `\r` to submit.
+- **Prompts are single-line.** With `useMux: true` the server delivers your text
+  and then Enter as two separate writes, so you do not append `\r` yourself. A
+  multi-line string breaks the agent's Ink-based input handling: send one line,
+  or split it across calls.
 - **Unwrap the envelope** before reading fields. `data` is not the response body.
 
 ## Publishing your integration