perf(api): bound worker pools and add telemetry

Share one configured PostgreSQL pool across worker repositories and make API and worker connection budgets explicit.

Add privacy-safe aggregate request, query, pool, sync, and outbox telemetry, a loopback-only representative load fixture, bounded worker shutdown, and focused regression and integration coverage.

Document the database-wide budget formula and defer pg_stat_statements activation to a reviewed migration and planned restart.

apps/api/src/workers/lifecycle.ts

@@ -0,0 +1,47 @@
+export interface WorkerLifecycleDependencies {
+  pollIntervalMs: number;
+  runTick: () => Promise<void>;
+  closePool: () => Promise<void>;
+  onTickFailure: (cause: unknown) => void;
+  graceMs?: number;
+}
+
+/** Owns worker tick scheduling and makes shutdown single-flight and bounded. */
+export class WorkerLifecycle {
+  private stopped = false;
+  private timer: NodeJS.Timeout | undefined;
+  private activeTick: Promise<void> | undefined;
+  private shutdownPromise: Promise<number> | undefined;
+  private readonly graceMs: number;
+
+  constructor(private readonly deps: WorkerLifecycleDependencies) { this.graceMs = deps.graceMs ?? 25_000; }
+
+  start(): void { if (!this.activeTick && !this.stopped) this.activeTick = this.tick(); }
+
+  shutdown(): Promise<number> {
+    if (!this.shutdownPromise) this.shutdownPromise = this.stop();
+    return this.shutdownPromise;
+  }
+
+  private async tick(): Promise<void> {
+    try { await this.deps.runTick(); }
+    catch (cause) { this.deps.onTickFailure(cause); }
+    finally {
+      if (!this.stopped) this.timer = setTimeout(() => { this.activeTick = this.tick(); }, this.deps.pollIntervalMs);
+    }
+  }
+
+  private async stop(): Promise<number> {
+    this.stopped = true;
+    if (this.timer) clearTimeout(this.timer);
+    const work = (async () => {
+      try { if (this.activeTick) await this.activeTick; await this.deps.closePool(); return 0; }
+      catch { return 1; }
+    })();
+    let timeout: NodeJS.Timeout | undefined;
+    const timedOut = new Promise<number>((resolve) => { timeout = setTimeout(() => resolve(1), this.graceMs); });
+    const result = await Promise.race([work, timedOut]);
+    if (timeout) clearTimeout(timeout);
+    return result;
+  }
+}