Harden async task flows and enhance analysis tooling

server/worker.ts

@@ -10,6 +10,7 @@ function sleep(ms: number) {
 }
 
 async function workOnce() {
+  await db.failExhaustedBackgroundTasks();
   await db.requeueStaleBackgroundTasks(new Date(Date.now() - ENV.backgroundTaskStaleMs));
 
   const task = await db.claimNextBackgroundTask(workerId);
@@ -17,6 +18,12 @@ async function workOnce() {
     return false;
   }
 
+  const heartbeatTimer = setInterval(() => {
+    void db.heartbeatBackgroundTask(task.id, workerId).catch((error) => {
+      console.error(`[worker] heartbeat failed for ${task.id}:`, error);
+    });
+  }, ENV.backgroundTaskHeartbeatMs);
+
   try {
     const result = await processBackgroundTask(task);
     if (result !== null) {
@@ -27,6 +34,8 @@ async function workOnce() {
     await db.failBackgroundTask(task.id, message);
     await db.failVisionTestRun(task.id, message);
     console.error(`[worker] task ${task.id} failed:`, error);
+  } finally {
+    clearInterval(heartbeatTimer);
   }
 
   return true;