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.

app/shared/src/commonTest/kotlin/iris/data/ChatStoreCacheTest.kt

@@ -2,10 +2,14 @@ package iris.data
 
 import iris.protocol.Frame
 import iris.protocol.IrisJson
+import iris.protocol.TYPE_TODO_UPDATE
 import iris.protocol.TYPE_TOOL_START
+import iris.protocol.TodoItem
+import iris.protocol.TodoUpdatePayload
 import iris.protocol.ToolStartPayload
 import kotlin.test.Test
 import kotlin.test.assertEquals
+import kotlin.test.assertNull
 
 class ChatStoreCacheTest {
     @Test
@@ -110,4 +114,42 @@ class ChatStoreCacheTest {
         val ids = store.lanes.value["default"]!!.map { it.id }
         assertEquals(ids.size, ids.toSet().size)
     }
+
+    @Test
+    fun todoUpdateSetsLaneListLastWriteWins() {
+        val store = ChatStore()
+        assertNull(store.todos.value["default"])
+        store.onFrame(todoFrame("default", listOf(TodoItem("1", "a", "in_progress"))))
+        assertEquals(listOf("1"), store.todos.value["default"]!!.map { it.id })
+        // A second update REPLACES the list (the gateway always sends the
+        // full list), and other lanes are untouched.
+        store.onFrame(
+            todoFrame(
+                "default",
+                listOf(TodoItem("1", "a", "completed"), TodoItem("2", "b", "pending")),
+            ),
+        )
+        store.onFrame(todoFrame("chan_7", listOf(TodoItem("9", "z", "pending"))))
+        assertEquals(listOf("1", "2"), store.todos.value["default"]!!.map { it.id })
+        assertEquals("completed", store.todos.value["default"]!![0].status)
+        assertEquals(listOf("9"), store.todos.value["chan_7"]!!.map { it.id })
+        // An empty list clears the lane (the agent dropped its plan).
+        store.onFrame(todoFrame("default", emptyList()))
+        assertNull(store.todos.value["default"])
+        assertEquals(listOf("9"), store.todos.value["chan_7"]!!.map { it.id })
+    }
+
+    private fun todoFrame(
+        chatId: String,
+        todos: List<TodoItem>,
+    ): Frame =
+        Frame(
+            type = TYPE_TODO_UPDATE,
+            chatId = chatId,
+            payload =
+                IrisJson.instance.encodeToJsonElement(
+                    TodoUpdatePayload.serializer(),
+                    TodoUpdatePayload(todos = todos),
+                ),
+        )
 }