feat(worker): Handler-Session nach Usage-Limit-Reset automatisch neu starten

Eine List-Handler-ConPTY-Session, die mitten in einer Phase stirbt, war bisher
ein stilles totes Tile: InteractiveTerminalViewModel.OnSessionProcessExited
setzte nur bei einem Tod innerhalb des 5s-Grace-Fensters ein sichtbares Banner.

Neu:
- HandlerRoundState (JSON unter ~/.claudeDo/handler-rounds.json, keine
  EF-Migration): Phase + Task-Set der laufenden Runde, geschrieben von
  BuildForMergeHelperAsync ("triage") und BuildForMergeHelperHandoffAsync.
  Ohne das existieren beide nur im transienten HandoffRequested-Broadcast.
- HandlerRestartCoordinator: entscheidet den Neustart, fail-closed. Beleg fuer
  "war das Usage-Limit" ist FiveHour.Utilization >= 95 zum Todeszeitpunkt --
  eine ConPTY-Session hat kein stdout, TaskRunner.IsUsageLimitMessage hat hier
  nichts zu lesen. Nur bei PowerUse (beide Keys), max ein Neustart pro Runde,
  Warten bis FiveHour.ResetsAt, dann HandoffRequested erneut broadcasten.
  Verbraucht kein Handoff-Budget (HandoffRoundTracker.Register wird nicht
  angefasst). WorkerLog-Zeilen beim Tod und beim Neustart.
- Ui meldet den Exit-Code (nur dort bekannt) via
  WorkerHub.ReportInteractiveSessionExited, ohne selbst zu filtern.

Sibling zu UsageLimitAutoContinueCoordinator, kein Umbau davon: der sieht nur
headless Runs.

src/ClaudeDo.Worker/Runner/InteractiveLaunchSpecService.cs

@@ -44,6 +44,7 @@ public sealed class InteractiveLaunchSpecService
     private readonly GitService _git;
     private readonly string _claudePath;
     private readonly HandoffRoundTracker _handoffRounds;
+    private readonly HandlerRoundState _roundState;
 
     public InteractiveLaunchSpecService(
         IDbContextFactory<ClaudeDoDbContext> dbFactory,
@@ -52,7 +53,8 @@ public sealed class InteractiveLaunchSpecService
         WorktreeManager wtManager,
         GitService git,
         WorkerConfig cfg,
-        HandoffRoundTracker handoffRounds)
+        HandoffRoundTracker handoffRounds,
+        HandlerRoundState roundState)
     {
         _dbFactory = dbFactory;
         _skillSeeder = skillSeeder;
@@ -61,6 +63,7 @@ public sealed class InteractiveLaunchSpecService
         _git = git;
         _claudePath = cfg.ClaudeBin;
         _handoffRounds = handoffRounds;
+        _roundState = roundState;
     }
 
     /// <summary>Builds a LaunchSpec for opening an interactive session in a task's worktree.
@@ -342,9 +345,20 @@ public sealed class InteractiveLaunchSpecService
             ["MCP_TOOL_TIMEOUT"] = McpToolTimeoutMs,
         };
 
+        // The opening round. Recorded so anything watching a handler run knows which round is live
+        // (the deferred-handoff follow-up needs that), but marked "triage" rather than a
+        // MergeHelperPhase value on purpose: there is no handoff spec for this phase, so
+        // HandlerRestartCoordinator will not reopen it.
+        _roundState.Save(new HandlerRound(handlerTaskId, TriagePhase, taskIds, DateTime.UtcNow));
+
         return new LaunchSpec(repoDir, resolvedClaude, args, env);
     }
 
+    /// <summary>The <see cref="HandlerRound.Phase"/> marker for the initial (dedupe/enhance) handler
+    /// session. Deliberately not a <see cref="MergeHelperPhase"/> value — that set is exactly the
+    /// phases <see cref="BuildForMergeHelperHandoffAsync"/> can rebuild.</summary>
+    public const string TriagePhase = "triage";
+
     // Builds the LaunchSpec for the fresh session a merge-helper run hands off to for the given
     // phase -- SAME handler task id as the run that called handoff_list_handler, so
     // HandlerBaseCommit/HandlerHeadCommit and the review range stay untouched; this never creates
@@ -449,6 +463,11 @@ public sealed class InteractiveLaunchSpecService
             ["MCP_TOOL_TIMEOUT"] = McpToolTimeoutMs,
         };
 
+        // Persist the round that is about to start. Phase + task set only exist in the transient
+        // HandoffRequested broadcast otherwise, so without this a dead tile cannot be reopened at
+        // the same phase with the same set (see HandlerRestartCoordinator).
+        _roundState.Save(new HandlerRound(taskId, nextPhase, survivingTaskIds, DateTime.UtcNow));
+
         return new LaunchSpec(repoDir, resolvedClaude, args, env);
     }