feat(worker): surface the handoff round budget in the merge-helper handoff brief

A handler session only learned the chain was capped when handoff_list_handler
threw at the end of its work, stranding open tasks. The round count already
lived in HandoffRoundTracker the whole time -- it just never reached the
brief. InteractiveLaunchSpecService now reads HandoffRoundTracker.GetState
(read-only, doesn't advance the round) and renders round N of MaxHandoffs
plus the remaining count into the handoff brief, replacing the old one-line
finalNote. The rejection error also names the next action (start a new
handler run) instead of just failing.

tests/ClaudeDo.Worker.Tests/Runner/InteractiveLaunchSpecServiceTests.cs

@@ -3,6 +3,7 @@ using ClaudeDo.Data.Git;
 using ClaudeDo.Data.Models;
 using ClaudeDo.Data.Repositories;
 using ClaudeDo.Worker.Config;
+using ClaudeDo.Worker.External;
 using ClaudeDo.Worker.Planning;
 using ClaudeDo.Worker.Runner;
 using ClaudeDo.Worker.Skills;
@@ -72,11 +73,12 @@ public sealed class InteractiveLaunchSpecServiceTests : IDisposable
             => Task.FromResult<IReadOnlyList<SessionSkillEntity>>(Installed);
     }
 
-    private InteractiveLaunchSpecService BuildService() =>
+    private InteractiveLaunchSpecService BuildService(HandoffRoundTracker? handoffRounds = null) =>
         new(_db.CreateFactory(), _seeder, _registry,
             new WorktreeManager(new GitService(), _db.CreateFactory(), new WorkerConfig(), NullLogger<WorktreeManager>.Instance),
             new GitService(),
-            new WorkerConfig { ClaudeBin = _claudeStubPath });
+            new WorkerConfig { ClaudeBin = _claudeStubPath },
+            handoffRounds ?? new HandoffRoundTracker());
 
     private async Task<string> SeedListAsync(string? workingDir = null, string name = "L")
     {
@@ -1043,7 +1045,13 @@ public sealed class InteractiveLaunchSpecServiceTests : IDisposable
 
         var beforeCount = await CountTasksAsync();
 
-        var svc = BuildService();
+        // In production, HandoffMcpTools.HandoffListHandler calls Register BEFORE the hub asks
+        // this service to build the spec -- simulate that here so the brief's round info is
+        // demonstrably read from HandoffRoundTracker, not recomputed.
+        var tracker = new HandoffRoundTracker();
+        tracker.Register(handlerTaskId, nextPhase);
+
+        var svc = BuildService(tracker);
         var spec = await svc.BuildForMergeHelperHandoffAsync(handlerTaskId, new[] { survivor }, nextPhase, CancellationToken.None);
         var sessionDir = TrackSessionDir(spec);
 
@@ -1090,6 +1098,10 @@ public sealed class InteractiveLaunchSpecServiceTests : IDisposable
         Assert.Contains(survivor, handoffBrief);
         Assert.Contains("phase 3", handoffBrief, StringComparison.OrdinalIgnoreCase);
 
+        // Round info always names the current round and the total cap -- this is the ONE
+        // Register call above, so round 1 of MaxHandoffs.
+        Assert.Contains($"round 1 of {HandoffRoundTracker.MaxHandoffs}", handoffBrief);
+
         if (expectFinalNote)
         {
             Assert.Contains("FINAL round", handoffBrief);