fix(ui): gate queueing on an open interactive ConPTY session

A task-based ConPTY session leaves the row Idle in the DB (sessions never
touch status), so nothing stopped the queue picker from claiming it too:
CanSendToQueue ignored HasInteractiveSession, and both TasksIslandViewModel.
SendToQueueAsync and MissionControlViewModel.EnqueueTaskAsync (drag-to-queue)
wrote Status=Queued straight via EF, bypassing TaskStateService entirely and
its manual/draft-child guards. That let an autonomous claude process spawn in
the same worktree a user was hand-editing in the ConPTY pane.

Add !HasInteractiveSession to CanSendToQueue, and route both UI enqueue paths
through IWorkerClient.SetTaskStatusAsync (worker hub -> TaskStateService.
EnqueueAsync) instead of raw EF writes. The interactive-session gate itself
stays in the UI: the worker has no notion of a UI-hosted ConPTY pane.

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

@@ -190,6 +190,27 @@ public class MissionControlViewModelTests : IDisposable
         await db.SaveChangesAsync();
     }
 
+    // Mirrors TaskStateService.EnqueueAsync writing to the same DB so the test can verify the
+    // resulting task state without the real worker process — EnqueueTaskAsync now delegates the
+    // actual status write to the worker hub instead of doing a raw EF write itself.
+    private sealed class QueueingWorkerClient : StubWorkerClient
+    {
+        private readonly Func<ClaudeDoDbContext> _newContext;
+        public List<string> QueuedTaskIds { get; } = new();
+
+        public QueueingWorkerClient(Func<ClaudeDoDbContext> newContext) => _newContext = newContext;
+
+        public override async Task SetTaskStatusAsync(string taskId, TaskStatus status)
+        {
+            QueuedTaskIds.Add(taskId);
+            await using var db = _newContext();
+            var entity = await db.Tasks.FirstOrDefaultAsync(t => t.Id == taskId);
+            if (entity is null) return;
+            entity.Status = status;
+            await db.SaveChangesAsync();
+        }
+    }
+
     [Fact]
     public async Task EnqueueTaskAsync_SetsTaskQueued_AndShowsInStrip()
     {
@@ -200,11 +221,12 @@ public class MissionControlViewModelTests : IDisposable
             await db.SaveChangesAsync();
         }
 
-        var worker = new FakeWorker();
+        var worker = new QueueingWorkerClient(NewContext);
         using var vm = BuildVm(worker);
 
         await vm.EnqueueTaskAsync("idleTask");
 
+        Assert.Equal(new[] { "idleTask" }, worker.QueuedTaskIds);
         Assert.True(vm.HasQueued);
         Assert.Contains(vm.Queued, q => q.Id == "idleTask");
 
@@ -213,6 +235,28 @@ public class MissionControlViewModelTests : IDisposable
         Assert.Equal(TaskStatus.Queued, entity.Status);
     }
 
+    [Fact]
+    public async Task EnqueueTaskAsync_TaskHasOpenConPtySession_DoesNotQueue()
+    {
+        await using (var db = NewContext())
+        {
+            db.Lists.Add(new ListEntity { Id = "L1", Name = "Work", CreatedAt = DateTime.UtcNow });
+            db.Tasks.Add(new TaskEntity { Id = "t1", ListId = "L1", Title = "Do the thing", Status = TaskStatus.Idle, CreatedAt = DateTime.UtcNow, SortOrder = 0 });
+            await db.SaveChangesAsync();
+        }
+
+        var worker = new QueueingWorkerClient(NewContext);
+        using var vm = BuildVm(worker);
+        await vm.OpenConPtySessionAsync("t1");
+
+        await vm.EnqueueTaskAsync("t1");
+
+        Assert.Empty(worker.QueuedTaskIds);
+        await using var verify = NewContext();
+        var entity = await verify.Tasks.FirstAsync(t => t.Id == "t1");
+        Assert.Equal(TaskStatus.Idle, entity.Status);
+    }
+
     private sealed class ThrowingLaunchSpecWorker : StubWorkerClient
     {
         public override Task<LaunchSpec> GetInteractiveLaunchSpecAsync(string taskId, CancellationToken ct = default)