feat(server,contracts,web): dashboard library counts and engine runs triggeredBy/multi-status filters

- GET /dashboard: automation.library {entities, movies, series, seasons,
  episodes, assets} and automation.slotSatisfiedRate; home media overview
  shows the counts instead of placeholders.
- GET /engine/runs: `status` accepts comma-separated values; new
  `triggeredBy` filter (comma-separated) evaluated server-side by scanning
  batches and paging with the last inspected row's cursor (scan cap 2000).
- Task stream: source filter and the "active" tab (running,pending) are now
  one paginated server query.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

apps/web/app/components/tasks/labels.ts

@@ -25,6 +25,13 @@ export const SOURCE_LABEL: Record<TaskSource, string> = {
   manual: "手动",
   agent: "Agent",
 };
+/** 来源 → 服务端 triggeredBy 筛选值(逗号分隔多值) */
+export const SOURCE_TRIGGERED_BY: Record<TaskSource, string> = {
+  schedule: "schedule",
+  event: "event",
+  manual: "user,api_key",
+  agent: "agent",
+};
 export function sourceOf(t: EngineTriggeredBy | null | undefined): TaskSource | null {
   if (!t) return null;
   if (t === "user" || t === "api_key") return "manual";