feat(worker): expose maxParallelExecutions in get_app_settings

The list-handler prompt (MergeHelperDefault) tells the handler to read
maxParallelExecutions via get_app_settings, but the DTO never carried
the field. Handler had to fall back to reading app_settings directly
from the DB on the 2026-07-29 E2E run.

src/ClaudeDo.Worker/CLAUDE.md

@@ -40,7 +40,7 @@ Interfaces (e.g. `IQueueWaker`, `IPrimeClock`, `ITaskStateService`) live in an `
   - `RunHistoryMcpTools` — `ListRuns`, `GetRun`, `GetTaskLog` (latest run's log, tail-capped at 256 KB)
   - `AgentMcpTools` — `ListAgents`
   - `LifecycleMcpTools` — `ResetFailedTask`
-  - `AppSettingsMcpTools` — `GetAppSettings` (read-only)
+  - `AppSettingsMcpTools` — `GetAppSettings` (read-only; includes `MaxParallelExecutions`)
   - `AttachmentMcpTools` — `AddTaskAttachment(taskId, fileName, textContent?|base64Content?)`, `ListTaskAttachments`, `RemoveTaskAttachment`. Re-attaching the same fileName overwrites; add/remove refuse on a Running task.
   - `ExternalMcpService` also exposes two daily-prep tools:
     - `GetDailyPrepCandidates` — returns Idle, non-blocked tasks in a git repo NOT excluded by `AppSettings.ReportExcludedPaths` and not already `IsMyDay`, plus the current Idle MyDay tasks and `maxTasks` (= `DailyPrepMaxTasks`). Repo-exclusion logic lives in the `DailyPrepFilter` helper (same file).

src/ClaudeDo.Worker/External/AppSettingsMcpTools.cs

@@ -8,6 +8,7 @@ namespace ClaudeDo.Worker.External;
 
 public sealed record AppSettingsReadDto(
     string DefaultModel, int DefaultMaxTurns, string DefaultPermissionMode,
+    int MaxParallelExecutions,
     string WorktreeStrategy, string? CentralWorktreeRoot,
     bool WorktreeAutoCleanupEnabled, int WorktreeAutoCleanupDays);
 
@@ -18,13 +19,14 @@ public sealed class AppSettingsMcpTools
 
     public AppSettingsMcpTools(IDbContextFactory<ClaudeDoDbContext> dbFactory) => _dbFactory = dbFactory;
 
-    [McpServerTool, Description("Read the worker's app-level defaults (model, max turns, permission mode, worktree strategy). Read-only.")]
+    [McpServerTool, Description("Read the worker's app-level defaults (model, max turns, permission mode, max parallel execution slots, worktree strategy). Read-only.")]
     public async Task<AppSettingsReadDto> GetAppSettings(CancellationToken cancellationToken)
     {
         using var ctx = await _dbFactory.CreateDbContextAsync(cancellationToken);
         var row = await new AppSettingsRepository(ctx).GetAsync(cancellationToken);
         return new AppSettingsReadDto(
             row.DefaultModel, row.DefaultMaxTurns, row.DefaultPermissionMode,
+            row.MaxParallelExecutions,
             row.WorktreeStrategy, row.CentralWorktreeRoot,
             row.WorktreeAutoCleanupEnabled, row.WorktreeAutoCleanupDays);
     }