feat(claude-do): Expose HandoffRoundTracker budget via an MCP tool (e.g. get_

The handoff-budget task (round/remaining/final now surfaced in the handoff.md brief via HandoffRoundTracker.GetStatus, wired through InteractiveLaunchSpecService.BuildForMergeHelperHandoffAsync) only reaches the session at the start of a handoff round. There is no way to query the current round/remaining budget for a handler task mid-session or from outside (e.g. the UI, or a script). Consider add

ClaudeDo-Task: 0a185f8e-823d-42fc-9a5b-97c5eb91c616

src/ClaudeDo.Worker/External/HandoffRoundTracker.cs

@@ -26,6 +26,20 @@ public sealed class HandoffRoundTracker
 
     public sealed record Result(bool Rejected, bool Coerced, string EffectivePhase, string? Error);
 
+    // Read-only budget lookup for a handler task that hasn't (yet) called HandoffListHandler --
+    // Round/Remaining/Final all report their untouched defaults instead of throwing, since "no
+    // handoff yet" is a normal state, not an error.
+    public sealed record Status(int Round, int Remaining, bool Final);
+
+    public Status GetStatus(string taskId)
+    {
+        if (!_states.TryGetValue(taskId, out var state))
+            return new Status(0, MaxHandoffs, false);
+
+        lock (state)
+            return new Status(state.Count, Math.Max(0, MaxHandoffs - state.Count), state.Sealed);
+    }
+
     public Result Register(string taskId, string nextPhase)
     {
         var state = _states.GetOrAdd(taskId, _ => new TaskState());