Send smaller first batch (5 features) for faster first paint

Subsequent batches use the normal batch_size (default 50). This
reduces server-side time-to-first-property by ~10x since only 5
features need to be serialized before the first yield.

tests/test_listing_geojson.py

@@ -302,3 +302,16 @@ class TestStreamingEndpoint:
                         assert feature["properties"]["qm"] is None
                         assert feature["properties"]["qmprice"] is None
 
+    def test_first_batch_is_smaller(self, client, mock_repository):
+        """Test that the first batch is smaller than subsequent batches for fast first paint."""
+        response = client.get("/api/listing_geojson/stream?listing_type=RENT&batch_size=50&limit=10")
+        lines = response.text.strip().split("\n")
+        messages = [json.loads(line) for line in lines]
+
+        batch_messages = [m for m in messages if m["type"] == "batch"]
+        assert len(batch_messages) >= 1
+
+        # First batch should contain FIRST_BATCH_SIZE (5) or fewer features
+        from api.app import FIRST_BATCH_SIZE
+        assert len(batch_messages[0]["features"]) <= FIRST_BATCH_SIZE
+