fix(home): server-owned growth window; expose days

Home omits growth_days; backend auto (or home_growth_days 1/7) picks
the window. Response includes days alongside growth_days. Growth榜 link
uses the returned days. Non-growth sorts treat omitted/auto as 7.

tests/test_web_server.py

@@ -108,8 +108,11 @@ def test_readonly_routes_and_static():
 
             status, _, payload = running.request("/api/videos")
             assert status == 200
-            items = json.loads(payload)["data"]["items"]
+            heat_payload = json.loads(payload)["data"]
+            items = heat_payload["items"]
             assert items and items[0]["aid"] == 102
+            # 非增长排序：省略 growth_days 时 days/growth_days 回落为 7，不做 7→1
+            assert heat_payload["days"] == heat_payload["growth_days"] == 7
 
             status, _, payload = running.json("/api/videos?year=2026")
             assert status == 200
@@ -120,6 +123,13 @@ def test_readonly_routes_and_static():
             assert status == 200
             assert payload["data"]["year"] == 2026
 
+            # 首页形态：省略 growth_days → 后端 auto，响应带 days/growth_days
+            status, _, payload = running.json("/api/videos?sort=growth&limit=6")
+            assert status == 200
+            growth = payload["data"]
+            assert growth["days"] == growth["growth_days"] == 1
+            assert growth["available"] is True
+
             status, _, payload = running.request("/api/ups")
             assert status == 200
             assert json.loads(payload)["data"]["sort"] == "efficiency"