perf(util): cut redundant work in per-frame detection consolidation (#23522)

video/detect.py runs these for every frame:

- get_cluster_candidates: used_boxes was a list with `in` membership tests
  inside the nested loop (O(n) per check). It is only ever membership-tested,
  so switching it to a set (O(1)) leaves output unchanged.
- get_consolidated_object_detections: area(current_box) was recomputed on
  every inner-loop iteration though it is loop-invariant; hoist it to one
  call per outer detection.

Both are bit-identical (verified against the previous implementations over
randomized inputs). Measured in the release image, get_cluster_candidates on
a frame of 30 detection boxes: 59.2 us -> 42.1 us (1.4x); the gain scales
with the number of boxes per frame.

Adds a partition-invariant test (every box index lands in exactly one
cluster).

Co-authored-by: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

frigate/test/test_video.py

@@ -82,6 +82,24 @@ class TestRegion(unittest.TestCase):
 
         assert len(cluster_candidates) == 2
 
+    def test_cluster_candidates_partition_boxes(self):
+        # every box index must appear in exactly one cluster (no box used twice,
+        # none dropped) - the invariant the used-box tracking enforces
+        boxes = [
+            (100, 100, 200, 200),
+            (202, 150, 252, 200),
+            (210, 160, 260, 210),
+            (900, 900, 950, 950),
+            (905, 905, 955, 955),
+        ]
+
+        cluster_candidates = get_cluster_candidates(
+            self.frame_shape, self.min_region_size, boxes
+        )
+
+        assigned = [idx for cluster in cluster_candidates for idx in cluster]
+        self.assertEqual(sorted(assigned), list(range(len(boxes))))
+
     def test_transliterate_to_latin(self):
         self.assertEqual(transliterate_to_latin("frégate"), "fregate")
         self.assertEqual(transliterate_to_latin("utilité"), "utilite")