feat(ui): Interactive chip for tasks with an open ConPTY session

A task driven by hand in Mission Control is Idle with an Active worktree, so its
lifecycle chip read "Parked" — indistinguishable from a task genuinely set aside.
The shell now mirrors Mission Control's open panes onto the rows, which show an
accent "Interactive" chip instead; tapping it surfaces Mission Control and
focuses that pane (the open command already dedupes by task id).

src/ClaudeDo.Ui/ViewModels/Islands/TaskRowViewModel.cs

@@ -35,6 +35,10 @@ public sealed partial class TaskRowViewModel : ViewModelBase
     [ObservableProperty] private bool _parentInView = true;
     [ObservableProperty] private int _roadblockCount;
     [ObservableProperty] private bool _isRefining;
+    // Set by the shell from Mission Control's open ConPTY panes: this task has a live hand-driven
+    // session, which outranks the persisted status on the lifecycle chip (an interactive task is
+    // typically Idle+Active-worktree, i.e. would otherwise read "Parked").
+    [ObservableProperty] private bool _hasInteractiveSession;
     // Set by the custom drag while this row is being dragged — drives the "grabbed" row style.
     [ObservableProperty] private bool _isDragging;
 
@@ -84,8 +88,10 @@ public sealed partial class TaskRowViewModel : ViewModelBase
     public bool IsOverdue   => ScheduledFor is { } d && d.Date < DateTime.Today && !Done;
     public bool IsRunning   => Status == TaskStatus.Running;
     public bool IsWaitingForReview => Status == TaskStatus.WaitingForReview;
-    // Parked = set aside from review: Idle but still holding its Active worktree (vs a plain Idle task).
-    public bool IsParked    => Status == TaskStatus.Idle && WorktreeState == ClaudeDo.Data.Models.WorktreeState.Active;
+    // Parked = set aside from review: Idle but still holding its Active worktree (vs a plain Idle
+    // task). A live ConPTY session is that same shape but not parked — it reads "Interactive".
+    public bool IsParked    => Status == TaskStatus.Idle && WorktreeState == ClaudeDo.Data.Models.WorktreeState.Active
+                               && !HasInteractiveSession;
     public bool IsQueued    => Status == TaskStatus.Queued && string.IsNullOrEmpty(BlockedByTaskId);
     public bool IsWaiting   => Status == TaskStatus.Queued && !string.IsNullOrEmpty(BlockedByTaskId);
     public bool CanRemoveFromQueue => IsQueued || HasQueuedSubtasks;
@@ -115,7 +121,14 @@ public sealed partial class TaskRowViewModel : ViewModelBase
     public string DiffDeletionsText => $"−{DiffDeletions}";
     public string StepsText         => Loc.T("vm.taskRow.stepsText", StepsCompleted, StepsCount);
 
-    public string StatusLabel => IsParked ? Loc.T("vm.taskStatus.parked") : Status switch
+    // Null on a plain status chip so no tooltip shows there — the chip is only actionable
+    // while a session is open.
+    public string? InteractiveChipTooltip
+        => HasInteractiveSession ? Loc.T("tasks.interactiveChipTip") : null;
+
+    public string StatusLabel
+        => HasInteractiveSession ? Loc.T("vm.taskStatus.interactive")
+         : IsParked ? Loc.T("vm.taskStatus.parked") : Status switch
     {
         TaskStatus.Idle             => Loc.T("vm.taskStatus.idle"),
         TaskStatus.Queued           => Loc.T("vm.taskStatus.queued"),
@@ -130,10 +143,14 @@ public sealed partial class TaskRowViewModel : ViewModelBase
 
     // A planning parent that is still Idle (Active planning, or Finalized-but-not-yet-queued)
     // already shows its state via the PLANNING/PLANNED badge next to the title. The lifecycle
-    // chip would read "Idle" (or "Parked"), which is misleading, so hide it in that case.
-    public bool ShowStatusChip => !(PlanningPhase != PlanningPhase.None && Status == TaskStatus.Idle);
+    // chip would read "Idle" (or "Parked"), which is misleading, so hide it in that case —
+    // unless there's a live session, where "Interactive" is exactly what the user needs to see.
+    public bool ShowStatusChip => HasInteractiveSession
+                                  || !(PlanningPhase != PlanningPhase.None && Status == TaskStatus.Idle);
 
-    public string StatusChipClass => (Status, IsBlocked: !string.IsNullOrEmpty(BlockedByTaskId)) switch
+    public string StatusChipClass => HasInteractiveSession
+        ? "interactive"
+        : (Status, IsBlocked: !string.IsNullOrEmpty(BlockedByTaskId)) switch
     {
         (TaskStatus.Running,            _) => "running",
         (TaskStatus.WaitingForReview,   _) => "review",
@@ -208,6 +225,15 @@ public sealed partial class TaskRowViewModel : ViewModelBase
 
     partial void OnIsRefiningChanged(bool value) => OnPropertyChanged(nameof(CanRefine));
 
+    partial void OnHasInteractiveSessionChanged(bool value)
+    {
+        OnPropertyChanged(nameof(IsParked));
+        OnPropertyChanged(nameof(StatusChipClass));
+        OnPropertyChanged(nameof(StatusLabel));
+        OnPropertyChanged(nameof(ShowStatusChip));
+        OnPropertyChanged(nameof(InteractiveChipTooltip));
+    }
+
     partial void OnHasQueuedSubtasksChanged(bool value)
     {
         OnPropertyChanged(nameof(CanRemoveFromQueue));

src/ClaudeDo.Ui/ViewModels/Islands/TasksIslandViewModel.cs

@@ -21,6 +21,9 @@ public sealed partial class TasksIslandViewModel : ViewModelBase, IDisposable
     private readonly Dictionary<string, bool> _expandedState = new();
     private ListNavItemViewModel? _currentList;
     private CancellationTokenSource? _loadCts;
+    // Task ids with a live ConPTY pane in Mission Control; kept here so rows loaded later still
+    // pick the flag up (see SyncInteractiveSessions).
+    private readonly HashSet<string> _interactiveSessionIds = new();
     private static readonly TaskListFilterRegistry _filters = new();
 
     public event EventHandler? SelectionChanged;
@@ -274,6 +277,7 @@ public sealed partial class TasksIslandViewModel : ViewModelBase, IDisposable
             {
                 var row = TaskRowViewModel.FromEntity(t);
                 row.ShowListChip = showListChip;
+                row.HasInteractiveSession = _interactiveSessionIds.Contains(row.Id);
                 Items.Add(row);
             }
 
@@ -441,6 +445,17 @@ public sealed partial class TasksIslandViewModel : ViewModelBase, IDisposable
         TasksChanged?.Invoke(this, EventArgs.Empty);
     }
 
+    /// <summary>Replaces the set of tasks that currently have an open interactive (ConPTY) session,
+    /// so their lifecycle chip reads "Interactive" instead of "Parked".</summary>
+    public void SyncInteractiveSessions(IEnumerable<string> taskIds)
+    {
+        _interactiveSessionIds.Clear();
+        foreach (var id in taskIds)
+            _interactiveSessionIds.Add(id);
+        foreach (var r in Items)
+            r.HasInteractiveSession = _interactiveSessionIds.Contains(r.Id);
+    }
+
     public bool CanReorder => _currentList?.Kind == ListKind.User;
 
     public void ClearDropHints()