fix(claude): retire leftover foreground rows when the next turn starts

A foreground `task_started` arriving with no turn open has no `result` coming
to retire it, so it sat in the strip indefinitely — with no per-row stop, since
foreground rows are not stoppable — and refused conversation commands behind an
instruction nobody could follow.

Settle on turn start as well as on `result`. This is cleanup only: visibility
never consults `startsTurn`, so a missed one degrades to today's behaviour and
can never switch the feature off. It shortens the row's life to the next turn;
the case where no further turn is ever sent is filed separately.

src/main/claude/claude-background-task-tracker.test.ts

@@ -114,6 +114,25 @@ describe('ClaudeBackgroundTaskTracker', () => {
     })
   })
 
+  it('retires a phantom foreground row when the next turn starts', () => {
+    // A foreground `task_started` with no turn open has no `result` coming to
+    // retire it, so it would sit in the strip — with no stop of its own — and
+    // refuse a conversation command. Turn start is the same evidence `result`
+    // is, and settling on it is cleanup only: nothing gates visibility on it.
+    const tracker = new ClaudeBackgroundTaskTracker()
+    tracker.observe(
+      system('task_started', {
+        task_id: 'phantom',
+        task_type: 'local_agent',
+        is_backgrounded: false
+      })
+    )
+    expect(tracker.state?.tasks).toEqual([{ id: 'phantom', kind: 'agent', stoppable: false }])
+
+    tracker.observe({ type: 'user' }, true)
+    expect(tracker.state).toBeNull()
+  })
+
   it('publishes bounded display details when a running task description changes', () => {
     const tracker = new ClaudeBackgroundTaskTracker()
     expect(

src/main/claude/claude-background-task-tracker.ts

@@ -89,6 +89,15 @@ export class ClaudeBackgroundTaskTracker {
   }
 
   observe(message: Record<string, unknown>, startsTurn = false): boolean {
+    // A new turn is the same evidence `result` is: nothing the previous turn
+    // left foreground is still that turn's work. This is CLEANUP ONLY — a row's
+    // visibility never depends on `startsTurn`, which is Orca's own
+    // dispatch-correlation bookkeeping and is false by design for undispatched
+    // turns, so a missed one degrades to the old behaviour and can never hide
+    // live work.
+    if (startsTurn) {
+      this.settleForegroundTasks()
+    }
     if (message.type === 'result') {
       this.settleForegroundTasks()
     } else if (message.type === 'system') {