feat(ui): interactive chat composer state on the session monitor VM

TaskMonitorViewModel gains IsInteractiveLive + ComposerDraft + SubmitComposer
(optimistic LogKind.User echo, then SendInteractiveMessageAsync) + StopInteractive,
driven by the InteractiveSessionStarted/Ended events. Since DetailsIslandViewModel
embeds this monitor, both task detail and Mission Control get the composer. Mission
Control auto-creates a monitor on InteractiveSessionStarted. Adds LogKind.User.

tests/ClaudeDo.Ui.Tests/ViewModels/TaskMonitorViewModelTests.cs

@@ -189,4 +189,112 @@ public class TaskMonitorViewModelTests : IDisposable
 
         Assert.False(vm.HasPendingQuestion);
     }
+
+    // ── Interactive composer ──────────────────────────────────────────────────
+
+    [Fact]
+    public void InteractiveStarted_ForSubscribedTask_SetsIsInteractiveLive()
+    {
+        var worker = new FakeWorker();
+        using var vm = Build(worker);
+        vm.SetTaskId("t1");
+
+        worker.RaiseInteractiveStarted("t1");
+
+        Assert.True(vm.IsInteractiveLive);
+        Assert.Equal("running", vm.AgentState);
+    }
+
+    [Fact]
+    public void InteractiveStarted_ForOtherTask_IsIgnored()
+    {
+        var worker = new FakeWorker();
+        using var vm = Build(worker);
+        vm.SetTaskId("t1");
+
+        worker.RaiseInteractiveStarted("other");
+
+        Assert.False(vm.IsInteractiveLive);
+    }
+
+    [Fact]
+    public void InteractiveEnded_ForSubscribedTask_ClearsIsInteractiveLive()
+    {
+        var worker = new FakeWorker();
+        using var vm = Build(worker);
+        vm.SetTaskId("t1");
+        worker.RaiseInteractiveStarted("t1");
+
+        worker.RaiseInteractiveEnded("t1");
+
+        Assert.False(vm.IsInteractiveLive);
+        Assert.Equal("done", vm.AgentState);
+    }
+
+    [Fact]
+    public void InteractiveEnded_ForOtherTask_IsIgnored()
+    {
+        var worker = new FakeWorker();
+        using var vm = Build(worker);
+        vm.SetTaskId("t1");
+        worker.RaiseInteractiveStarted("t1");
+
+        worker.RaiseInteractiveEnded("other");
+
+        Assert.True(vm.IsInteractiveLive); // unchanged
+    }
+
+    [Fact]
+    public void SubmitComposerCommand_CanExecute_FalseWhenNotLive()
+    {
+        var worker = new FakeWorker();
+        using var vm = Build(worker);
+        vm.SetTaskId("t1");
+        vm.ComposerDraft = "hello";
+
+        Assert.False(vm.SubmitComposerCommand.CanExecute(null));
+    }
+
+    [Fact]
+    public void SubmitComposerCommand_CanExecute_FalseWhenLiveButDraftWhitespace()
+    {
+        var worker = new FakeWorker();
+        using var vm = Build(worker);
+        vm.SetTaskId("t1");
+        worker.RaiseInteractiveStarted("t1");
+        vm.ComposerDraft = "   ";
+
+        Assert.False(vm.SubmitComposerCommand.CanExecute(null));
+    }
+
+    [Fact]
+    public void SubmitComposerCommand_CanExecute_TrueWhenLiveAndDraftSet()
+    {
+        var worker = new FakeWorker();
+        using var vm = Build(worker);
+        vm.SetTaskId("t1");
+        worker.RaiseInteractiveStarted("t1");
+        vm.ComposerDraft = "hello";
+
+        Assert.True(vm.SubmitComposerCommand.CanExecute(null));
+    }
+
+    [Fact]
+    public async Task SubmitComposer_AddsUserLogLine_ClearsDraft_CallsClient()
+    {
+        var worker = new FakeWorker();
+        using var vm = Build(worker);
+        vm.SetTaskId("t1");
+        worker.RaiseInteractiveStarted("t1");
+        vm.ComposerDraft = "do the thing";
+
+        await vm.SubmitComposerCommand.ExecuteAsync(null);
+
+        Assert.Single(worker.SentInteractive);
+        Assert.Equal(("t1", "do the thing"), worker.SentInteractive[0]);
+        Assert.Equal(string.Empty, vm.ComposerDraft);
+        Assert.Single(vm.Log);
+        Assert.Equal(LogKind.User, vm.Log[0].Kind);
+        Assert.Equal("do the thing", vm.Log[0].Text);
+    }
 }