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/test/operations.runner.test.ts

@@ -7,7 +7,7 @@ import { loadWorkerConfig } from '../src/workers/config.js';
 
 const summary={releasedPacks:0,streakMilestones:0,digests:0,packChanges:0,weeklySummaries:0,unpairedReminders:0,catchupReminders:0,streakReminders:0,daresExpired:0};
 function repository(items:OperationItem[]):OperationsRepository {
-  return {produce:vi.fn(async()=>summary),claim:vi.fn(async()=>items),complete:vi.fn(async()=>undefined),fail:vi.fn(async()=>undefined),
+  return {produce:vi.fn(async()=>summary),claim:vi.fn(async()=>items),complete:vi.fn(async()=>undefined),fail:vi.fn(async()=>undefined),outboxState:vi.fn(async()=>({due:items.length,oldestDueAgeSeconds:0})),
     message:vi.fn(async()=>null),classifierConfig:vi.fn(async()=>null),classify:vi.fn(async()=>undefined),close:vi.fn(async()=>undefined)};
 }
 
@@ -71,4 +71,11 @@ describe('worker configuration',()=>{
       discordWebhookUrl:undefined,
     });
   });
+
+  it('uses a distinct bounded pool configuration for the worker process',()=>{
+    expect(loadWorkerConfig({
+      DATABASE_URL:'postgresql://sauci:test@localhost:5432/sauci',
+      DATABASE_POOL_MAX:'3', DATABASE_POOL_IDLE_TIMEOUT_MS:'1200', DATABASE_POOL_CONNECTION_TIMEOUT_MS:'3400',
+    }).databasePool).toEqual({max:3,idleTimeoutMillis:1200,connectionTimeoutMillis:3400});
+  });
 });