feat(FN-5479): fix identity-guard merger bypass on detached HEAD and gate l

The merge delivers the FN-5483 identity-guard bypass for merger-driven commits on detached HEAD, plus Steps 2 and 6 of FN-5479 which gate the limbo counter by enqueue acceptance and document the associated invariant. It also restores the dashboard's PWA and theme-boot contract in index.html. New reg

Fusion-Task-Id: FN-5479

packages/engine/src/__tests__/reliability-interactions/completion-handoff-limbo.test.ts

@@ -123,4 +123,29 @@ describe("FN-4999 reliability interactions: completion-handoff-limbo", () => {
       .filter((value: unknown) => typeof value === "number");
     expect(increments).toEqual([1, 2, 3]);
   });
+
+  it("FN-5479: does not consume limbo recovery budget when merge requeue is not accepted", async () => {
+    const task = makeTask({
+      status: undefined,
+      review: undefined,
+      reviewState: undefined,
+      mergeDetails: undefined,
+      completionHandoffLimboRecoveryCount: 2,
+      log: [{ action: "Task marked done by agent", timestamp: new Date(Date.now() - 6 * 60_000).toISOString() } as any],
+    });
+    const store = createStore(task);
+    const manager = new SelfHealingManager(store, {
+      rootDir: "/repo",
+      enqueueMerge: vi.fn(() => false),
+      requeueForAutoMerge: vi.fn(() => false),
+    });
+
+    await manager.recoverCompletionHandoffLimbo();
+
+    expect(store.enqueueMergeQueue).toHaveBeenCalledWith("FN-4999-T");
+    expect(store.updateTask).not.toHaveBeenCalledWith("FN-4999-T", expect.objectContaining({ completionHandoffLimboRecoveryCount: 3 }));
+    expect(store.recordRunAuditEvent).not.toHaveBeenCalledWith(expect.objectContaining({ mutationType: "task:auto-recover-completion-handoff-limbo" }));
+    expect(store.logEntry).not.toHaveBeenCalledWith("FN-4999-T", expect.stringMatching(/Auto-recovered \(FN-4999\)/));
+    expect(store._get().completionHandoffLimboRecoveryCount).toBe(2);
+  });
 });