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.

src/ClaudeDo.Worker/Program.cs

@@ -94,6 +94,7 @@ builder.Services.AddSingleton<PendingQuestionRegistry>();
 builder.Services.AddSingleton<IRepoCloner, GitRepoCloner>();
 builder.Services.AddSingleton<ISessionSkillRegistry, SessionSkillRegistry>();
 builder.Services.AddSingleton<ISessionSkillSeeder, SessionSkillSeeder>();
+builder.Services.AddSingleton<HandoffRoundTracker>();
 builder.Services.AddSingleton<InteractiveLaunchSpecService>();
 builder.Services.AddSingleton<TaskRunner>();
 builder.Services.AddSingleton<WorktreeMaintenanceService>();
@@ -335,6 +336,7 @@ if (cfg.ExternalMcpPort > 0)
     Share<InteractiveReviewSubmissionService>();
     Share<AttachmentStore>();
     Share<FindingsStore>();
+    Share<HandoffRoundTracker>();
 
     externalBuilder.Services.AddScoped<ClaudeDoDbContext>(sp =>
         sp.GetRequiredService<IDbContextFactory<ClaudeDoDbContext>>().CreateDbContext());
@@ -342,7 +344,6 @@ if (cfg.ExternalMcpPort > 0)
     externalBuilder.Services.AddScoped<ListRepository>();
     externalBuilder.Services.AddScoped<TaskRunRepository>();
     externalBuilder.Services.AddScoped<TaskAttachmentRepository>();
-    externalBuilder.Services.AddSingleton<HandoffRoundTracker>();
     externalBuilder.Services.AddScoped<FindingsStoreLocator>();
     externalBuilder.Services.AddScoped<ExternalMcpService>();
     externalBuilder.Services.AddScoped<MergeMcpTools>();