feat(worker): wire list-handler phase parameter through handoff chain

Threads a nextPhase parameter (wait/merge/wait_final/merge_final, validated
by the new MergeHelperPhase) from handoff_list_handler through
HubBroadcaster/WorkerHub into InteractiveLaunchSpecService, which now picks
the next session's system prompt (MergeHelperWait/MergeHelperMerge) and
model (HandlerWaitAlias/HandlerMergeAlias) from it instead of hardcoding the
old two-phase Execute prompt -- this also fixes a build break left by the
prior prompt-split task, which removed PromptKind.MergeHelperExecute without
updating its only caller.

Also sets --model/--effort/--permission-mode explicitly for every list-handler
session (Triage included) via PermissionModeResolver instead of inheriting the
CLI's ambient model and hardcoding "auto", and adds Task to the merge-helper
allowlist so the Merge phase can delegate diff reviews to subagents.

src/ClaudeDo.Worker/External/HandoffMcpTools.cs

@@ -1,11 +1,12 @@
 using System.ComponentModel;
 using ClaudeDo.Data.Repositories;
 using ClaudeDo.Worker.Hub;
+using ClaudeDo.Worker.Runner;
 using ModelContextProtocol.Server;
 
 namespace ClaudeDo.Worker.External;
 
-public sealed record HandoffListHandlerResult(bool Requested, string TaskId, int SurvivingCount);
+public sealed record HandoffListHandlerResult(bool Requested, string TaskId, int SurvivingCount, string NextPhase);
 
 [McpServerToolType]
 public sealed class HandoffMcpTools
@@ -20,16 +21,22 @@ public sealed class HandoffMcpTools
     }
 
     [McpServerTool, Description(
-        "Call at the end of Phase 2 of the list handler (\"Let Claude handle it\") to hand this run off " +
-        "to a fresh ConPTY session that carries out Phases 3-5, without dragging along this session's " +
-        "dedupe/rewrite context. Reuses the SAME handler task -- no new task is created, and " +
-        "HandlerBaseCommit is untouched. The current tile stays open; you must end your own turn " +
-        "immediately after calling this.")]
+        "Call at the end of a list-handler (\"Let Claude handle it\") phase to hand this run off to a " +
+        "fresh ConPTY session that carries out the next phase, without dragging along this session's " +
+        "own context. Reuses the SAME handler task -- no new task is created, and HandlerBaseCommit is " +
+        "untouched. nextPhase picks the next session's role: \"wait\" (queue + wait; the normal handoff " +
+        "after triage) or \"merge\" (review + merge; the normal handoff after wait) -- \"wait_final\"/" +
+        "\"merge_final\" are only for a merge session that started reruns and must eventually stop the " +
+        "chain instead of restarting again. An unrecognized value is rejected. The current tile stays " +
+        "open; you must end your own turn immediately after calling this.")]
     public async Task<HandoffListHandlerResult> HandoffListHandler(
         [Description("This session's own handler task id.")] string taskId,
         [Description("The tasks that made it past dedupe, in the order to run them.")] IReadOnlyList<string> survivingTaskIds,
-        CancellationToken cancellationToken)
+        [Description("Next session's phase: wait | merge | wait_final | merge_final.")] string nextPhase = "wait",
+        CancellationToken cancellationToken = default)
     {
+        MergeHelperPhase.Validate(nextPhase);
+
         if (survivingTaskIds.Count == 0)
             throw new InvalidOperationException("survivingTaskIds must contain at least one task id.");
 
@@ -40,7 +47,7 @@ public sealed class HandoffMcpTools
             _ = await _tasks.GetByIdAsync(id, cancellationToken)
                 ?? throw new InvalidOperationException($"Task {id} not found.");
 
-        await _broadcaster.HandoffRequested(taskId, survivingTaskIds);
-        return new HandoffListHandlerResult(true, taskId, survivingTaskIds.Count);
+        await _broadcaster.HandoffRequested(taskId, survivingTaskIds, nextPhase);
+        return new HandoffListHandlerResult(true, taskId, survivingTaskIds.Count, nextPhase);
     }
 }