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

README.zh-CN.md

@@ -802,6 +802,8 @@ Codeman 会注册 Claude Code hook，它们 `POST /api/hook-event`（`permission
 | `POST` | `/api/clipboard`                | 把文本推送到所有已连接浏览器（`{text}`） |
 | `GET`  | `/api/sessions/:id/run-summary` | 时间线 + 统计                            |
 
+> **想在 Codeman 之上做集成？**[`docs/extending-codeman.md`](docs/extending-codeman.md)（英文）是集成指南：把你自己的界面作为标签页嵌入、订阅 SSE 事件流以便在 agent 需要你时做出响应、用脚本驱动 Codeman，以及动手前值得先了解的那些坑。Codeman 刻意不提供插件运行时，所以一个集成就是你自己的进程在讲 HTTP。
+
 ---
 
 ## 架构

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