docs: tighten the inbox, push and idle-detection wording

Follow-up to the previous commit, after a fact check against the code.

- Answer surfaces: the header bell answers Claude prompts, the phone
  strip only Claude dialogs (and only with the inbox on), and push
  Approve/Deny only a Claude permission prompt (PUSH_EVENT_MAP gives
  actions to permission_prompt alone). README, its Chinese mirror, the
  notifications page and the phone guide now say so.
- Antigravity and Grok Build: after the 3 s launch settle, idle is armed
  only by Claude's prompt marker and working only by a braille spinner,
  so "idle when output stops changing" was wrong. The wiki, the grok
  guide and the API reference now call their status unreliable.
- DeepSeek Harness: its idle and working reports become stop and
  agent_working, which drive respawn, waits and the inbox but not the
  session's own working/idle display. Keeping Agents Running says that,
  and that the respawn path needs the status bridge.
- The wait section of the API reference no longer calls exit the only
  dependable signal for screen-checked modes; the inbox page names how
  Codex and DeepSeek items clear; Core Concepts and Hooks And
  Integrations no longer call DeepSeek "the one" exception; Agent CLIs
  notes that Codex dialogs still raise the red alert; the inbox design
  doc notes the alert-only items.
- Skill: stop and blocked list deepseek, and SKILL.md no longer says
  codex has neither a transcript nor blocked. Mirrored with
  scripts/sync-plugin.mjs.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

README.md

@@ -277,7 +277,7 @@ Hit start — Codeman spawns the CLI via a real PTY and streams it to your brows
 - **Paste, drop or attach images, videos and documents** (PDF, Office files, zip and plain text) directly into the session. They are saved in a hidden `.codeman-uploads/` folder in the workspace (it ignores itself in git and is swept after 7 days), and the file's path lands on your prompt, unsent.
 - **Voice input** — `Ctrl+Shift+V` (Deepgram Nova-3, or this machine's Claude Code login with no API key; auto-silence stop).
 - **Attachments** — register external files/docs and preview Office/PDF inline; any file path an agent prints is clickable, in the terminal and in the chat view, including `~/` and relative paths and paths broken across lines. An `.html` report opens as a real page, Markdown opens rendered, and a folder opens as a grid of its files.
-- **When it needs you** — the tab turns yellow (waiting for input) or red (a question is blocking). The **Approvals Inbox** _(opt-in)_ queues the prompts waiting on you from Claude Code, Codex and DeepSeek Harness sessions in one list. Claude prompts are answerable from the header bell, the phone home screen or a push notification's Approve/Deny buttons; Codex and DeepSeek items are alerts that tell you to answer in the terminal, and prompts from the other CLIs do not enter it. 🧠 **Read My Mind** _(opt-in)_ drafts your next prompt from the case's goals and recent work.
+- **When it needs you** — the tab turns yellow (waiting for input) or red (a question is blocking). The **Approvals Inbox** _(opt-in)_ queues the prompts waiting on you from Claude Code, Codex and DeepSeek Harness sessions in one list. Claude prompts are answerable from the header bell, Claude dialogs also from the phone home screen, and a Claude permission prompt also from a push notification's Approve/Deny buttons; Codex and DeepSeek items are alerts that tell you to answer in the terminal, and prompts from the other CLIs do not enter it. 🧠 **Read My Mind** _(opt-in)_ drafts your next prompt from the case's goals and recent work.
 - **Copy what you see** — `Shift+drag` selects text even while the CLI owns the mouse, right-click copies it, and Auto Copy _(opt-in)_ copies a selection the moment you release it. A program that copies with OSC 52 (Claude Code's `/copy`, a tmux yank, vim) puts the text on your browser's clipboard too.
 
 ### 5. Make it autonomous