fix(worker): reap idle interactive sessions so they don't pile up

Interactive/streaming sessions are persistent claude.exe processes that
wait on stdin and never exit on their own. The only teardown was an
explicit StopInteractiveSession from the UI — there is no client-disconnect
or shutdown sweep — so an abandoned chat (UI closed, navigated away,
crashed) kept its claude.exe (+ conhost) alive for the worker's whole
lifetime. Under a long-running autostart worker these accumulate to dozens
of orphaned child processes.

LiveSessionRegistry now tracks per-session activity (Touch on every output
line and user action) and exposes ReapIdleAsync, which stops sessions idle
past a timeout while skipping any with a turn in flight. IdleSessionReaper
(BackgroundService) sweeps every 5 min; idle timeout defaults to 30 min,
configurable via interactive_idle_timeout_minutes (0 disables).

tests/ClaudeDo.Worker.Tests/Runner/LiveSessionRegistryTests.cs

@@ -8,7 +8,7 @@ public sealed class LiveSessionRegistryTests
     private sealed class FakeLiveSession : ILiveSession
     {
         public bool StopCalled { get; private set; }
-        public bool IsTurnInFlight => false;
+        public bool IsTurnInFlight { get; set; }
 
         public Task SendUserMessageAsync(string text, CancellationToken ct) => Task.CompletedTask;
         public Task RemoveQueuedAsync(string text, CancellationToken ct) => Task.CompletedTask;
@@ -90,4 +90,56 @@ public sealed class LiveSessionRegistryTests
         var registry = new LiveSessionRegistry();
         await registry.StopAsync("no-such-task"); // should not throw
     }
+
+    [Fact]
+    public async Task ReapIdleAsync_StopsAndRemovesIdleSession()
+    {
+        var registry = new LiveSessionRegistry();
+        var session = new FakeLiveSession();
+        registry.Register("task-1", session);
+
+        // Sweep "now" is an hour past registration, well beyond the 30-min idle window.
+        var reaped = await registry.ReapIdleAsync(DateTime.UtcNow.AddMinutes(60), TimeSpan.FromMinutes(30));
+
+        Assert.Contains("task-1", reaped);
+        Assert.True(session.StopCalled);
+        Assert.False(registry.TryGet("task-1", out _));
+    }
+
+    [Fact]
+    public async Task ReapIdleAsync_KeepsRecentlyActiveSession()
+    {
+        var registry = new LiveSessionRegistry();
+        var session = new FakeLiveSession();
+        registry.Register("task-1", session);
+
+        var reaped = await registry.ReapIdleAsync(DateTime.UtcNow, TimeSpan.FromMinutes(30));
+
+        Assert.Empty(reaped);
+        Assert.False(session.StopCalled);
+        Assert.True(registry.TryGet("task-1", out _));
+    }
+
+    [Fact]
+    public async Task ReapIdleAsync_SkipsSessionWithTurnInFlight()
+    {
+        var registry = new LiveSessionRegistry();
+        var session = new FakeLiveSession { IsTurnInFlight = true };
+        registry.Register("task-1", session);
+
+        // Idle long enough to reap, but a turn is in flight → must be left alone.
+        var reaped = await registry.ReapIdleAsync(DateTime.UtcNow.AddMinutes(60), TimeSpan.FromMinutes(30));
+
+        Assert.Empty(reaped);
+        Assert.False(session.StopCalled);
+        Assert.True(registry.TryGet("task-1", out _));
+    }
+
+    [Fact]
+    public async Task ReapIdleAsync_NoSessions_ReturnsEmpty()
+    {
+        var registry = new LiveSessionRegistry();
+        var reaped = await registry.ReapIdleAsync(DateTime.UtcNow, TimeSpan.FromMinutes(30));
+        Assert.Empty(reaped);
+    }
 }