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/HandoffMcpTools.cs

@@ -11,6 +11,8 @@ namespace ClaudeDo.Worker.External;
 // reflects the effective (post-coercion) value in that case.
 public sealed record HandoffListHandlerResult(bool Requested, string TaskId, int Number, int SurvivingCount, string NextPhase, bool Coerced = false);
 
+public sealed record HandoffStatusResult(string TaskId, int Number, int Round, int Remaining, bool Final);
+
 [McpServerToolType]
 public sealed class HandoffMcpTools
 {
@@ -66,4 +68,24 @@ public sealed class HandoffMcpTools
         await _broadcaster.HandoffRequested(taskId, survivingTaskIds, round.EffectivePhase);
         return new HandoffListHandlerResult(true, taskId, task.Number, survivingTaskIds.Count, round.EffectivePhase, round.Coerced);
     }
+
+    [McpServerTool, Description(
+        "Read-only lookup of a handler task's handoff-round budget (round already used, rounds " +
+        "remaining before handoff_list_handler starts coercing to a _final phase, and whether the " +
+        "chain is already sealed by a completed merge_final round) -- for checking the budget mid-" +
+        "session or from outside a handoff, instead of only seeing it once at the start of a round. " +
+        "A task that never called handoff_list_handler reports round 0, its full remaining budget, " +
+        "and final=false. In-memory only, same as the tracker itself: a worker restart resets it." +
+        McpToolDocs.TaskNumberHint)]
+    public async Task<HandoffStatusResult> GetHandoffStatus(
+        [Description("The handler task's own id.")] string taskId,
+        CancellationToken cancellationToken = default)
+    {
+        taskId = await TaskIdResolver.ResolveAsync(_tasks, taskId, cancellationToken);
+        var task = await _tasks.GetByIdAsync(taskId, cancellationToken)
+            ?? throw new InvalidOperationException($"Task {taskId} not found.");
+
+        var status = _rounds.GetStatus(taskId);
+        return new HandoffStatusResult(taskId, task.Number, status.Round, status.Remaining, status.Final);
+    }
 }

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());