feat(HAI-001): wire status updates in triage processor

packages/engine/src/triage.ts

@@ -99,6 +99,8 @@ export class TriageProcessor {
     console.log(`[triage] Specifying ${task.id}: ${task.title}`);
     this.options.onSpecifyStart?.(task);
 
+    await this.store.setStatus(task.id, "specifying");
+
     try {
       // Get the full task detail including current prompt
       const detail = await this.store.getTask(task.id);
@@ -130,6 +132,7 @@ export class TriageProcessor {
       }
     } catch (err: any) {
       console.error(`[triage] ✗ ${task.id} specification failed:`, err.message);
+      await this.store.setStatus(task.id, "idle");
       this.options.onSpecifyError?.(task, err);
     } finally {
       this.processing.delete(task.id);