Live agent todo list: compact scrollable strip above the composer

Add a todo.update frame (server->app) carrying the agent's full current
todo list. The gateway emits it whenever the hermes todo tool completes
(the tool result is authoritative even for merge writes) and re-sends a
snapshot right after hello so a reconnecting device re-learns the plan.
Ephemeral: never outboxed.

The app renders it as a compact strip above the composer (max 3 lines,
the rest scrollable) mirroring the hermes desktop composer status stack:
pending = hollow ring, in_progress = spinner, completed = green check,
cancelled = struck through. It auto-scrolls to the current task whenever
the active task changes, and hides itself once the list is empty or fully
resolved.

docs/04-wire-protocol.md

@@ -140,6 +140,31 @@ short tail (full output is not streamed — it lives in agent history).
 `emoji` — e.g. `read_file` 📖, `write_file` ✍️, `terminal` 💻). Omitted when
 the tool is unknown, so the app falls back to its own default glyph.
 
+### `todo.update`
+
+The agent's **full current todo list** for a chat/thread lane (last-write-wins).
+Emitted whenever the `todo` tool completes — the tool *result* is the
+authoritative list, which also covers `merge` writes (whose args carry only
+the changed items) and read-only calls — and, as a **snapshot**, right after
+`hello` when a device opens its event stream.
+
+```json
+{"type":"todo.update","chat_id":"default","thread_id":null,"payload":{
+   "todos":[
+     {"id":"1","content":"Scaffold the module","status":"completed"},
+     {"id":"2","content":"Wire the store","status":"in_progress"},
+     {"id":"3","content":"Add tests","status":"pending"}
+   ]}}
+```
+
+`status` is one of `pending | in_progress | completed | cancelled`. The frame
+is **ephemeral**: it is never outboxed, so a reconnecting device learns the
+current list from the snapshot (not a replay), and a gateway restart drops it
+(the agent re-emits on the next `todo` call). The app renders it as a compact
+scrollable strip above the composer (max 3 lines; auto-scrolls to the item
+whose status just changed) and hides it once the list is empty or fully
+resolved.
+
 ### `typing` / `typing.stop`
 
 ```json