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/server/test/auth-settings/admin-api.test.ts

@@ -298,6 +298,9 @@ describe.skipIf(!hasPg)("W2-A 管理 API(真实 PG)", () => {
       expect(p2.data.items.map((r: { id: string }) => r.id)).toEqual(["r1"]);
       expect(p2.data.nextCursor).toBeNull();
       expect((await admin("GET", "/engine/runs?status=bogus")).status).toBe(422);
+      const multi = await json(await admin("GET", "/engine/runs?status=running,pending"));
+      expect(multi.data.items.map((r: { id: string }) => r.id)).toEqual(["r4", "r3"]);
+      expect((await admin("GET", "/engine/runs?status=running,bogus")).status).toBe(422);
     });
 
     it("run 详情:step attempts + signals;敏感字段脱敏,不返回 config/context", async () => {