feat(list-handler): hand off to a fresh session after Phase 2

The merge-helper ("Let Claude handle it") system prompt now calls a new
handoff_list_handler MCP tool once every surviving task is enhanced,
instead of continuing into Phases 3-5 in the same session -- avoiding
paying for Phases 0-2's dedupe/rewrite context on every polling round of
the run/review/merge phases.

The tool broadcasts HandoffRequested; Mission Control opens a second
ConPTY tile for the SAME handler task id (no new task, HandlerBaseCommit
untouched) running a fresh handoff brief that starts at Phase 3. The
original tile stays open. Adds PromptKind.MergeHelperHandoff,
InteractiveLaunchSpecService.BuildForMergeHelperHandoffAsync, and the
GetMergeHelperHandoffLaunchSpec hub method.

src/ClaudeDo.Worker/External/HandoffMcpTools.cs

@@ -0,0 +1,44 @@
+using System.ComponentModel;
+using ClaudeDo.Data.Repositories;
+using ClaudeDo.Worker.Hub;
+using ModelContextProtocol.Server;
+
+namespace ClaudeDo.Worker.External;
+
+public sealed record HandoffListHandlerResult(bool Requested, string TaskId, int SurvivingCount);
+
+[McpServerToolType]
+public sealed class HandoffMcpTools
+{
+    private readonly TaskRepository _tasks;
+    private readonly HubBroadcaster _broadcaster;
+
+    public HandoffMcpTools(TaskRepository tasks, HubBroadcaster broadcaster)
+    {
+        _tasks = tasks;
+        _broadcaster = broadcaster;
+    }
+
+    [McpServerTool, Description(
+        "End of Phase 2 for the list handler (\"Let Claude handle it\"): hand this run off to a fresh " +
+        "ConPTY session that carries out Phases 3-5, without dragging along this session's dedupe/rewrite " +
+        "context. taskId is this session's own handler task id; survivingTaskIds are the tasks that made " +
+        "it past dedupe, in the order to run them. Reuses the SAME handler task -- no new task is created, " +
+        "and HandlerBaseCommit is untouched. The current tile stays open; end your own turn after calling this.")]
+    public async Task<HandoffListHandlerResult> HandoffListHandler(
+        string taskId, IReadOnlyList<string> survivingTaskIds, CancellationToken cancellationToken)
+    {
+        if (survivingTaskIds.Count == 0)
+            throw new InvalidOperationException("survivingTaskIds must contain at least one task id.");
+
+        _ = await _tasks.GetByIdAsync(taskId, cancellationToken)
+            ?? throw new InvalidOperationException($"Task {taskId} not found.");
+
+        foreach (var id in survivingTaskIds)
+            _ = await _tasks.GetByIdAsync(id, cancellationToken)
+                ?? throw new InvalidOperationException($"Task {id} not found.");
+
+        await _broadcaster.HandoffRequested(taskId, survivingTaskIds);
+        return new HandoffListHandlerResult(true, taskId, survivingTaskIds.Count);
+    }
+}