feat: home growth auto(7→1) and hourly recent-video snapshot

- Add analytics.home_growth_days (auto|1|7); API growth_days=auto tries 7 then 1
- Homepage shows active window and growth-board link; clearer empty reason
- New snapshot_recent scheduler task (schedule.recent_snapshot_minutes/days)
- run_recent_videos refreshes new aids only; never touches completed/backup
- Full 00:01 job keeps ok=1 skip (covers hourly refresh within 1h); mutex with recent

reaction_board/web/server.py

@@ -373,7 +373,7 @@ border-color:#3a2c22;color:#f3e9dc}button{background:#e9b97c;color:#2a1a10}}
                 sort=_param(query, "sort", "heat"),
                 within_days=_optional_int(query, "within_days"),
                 year=_year_param(query),
-                growth_days=_int_param(query, "growth_days", 7, 1, 365),
+                growth_days=_growth_days_param(query),
                 folder_id=_optional_int(query, "folder"),
                 q=_optional_str(query, "q"),
                 page=_int_param(query, "page", 1, 1, 1_000_000),
@@ -422,7 +422,7 @@ border-color:#3a2c22;color:#f3e9dc}button{background:#e9b97c;color:#2a1a10}}
                 sort=_param(query, "sort", "heat"),
                 within_days=_optional_int(query, "within_days"),
                 year=_year_param(query),
-                growth_days=_int_param(query, "growth_days", 7, 1, 365),
+                growth_days=_growth_days_param(query),
                 folder_id=_optional_int(query, "folder"),
                 q=_optional_str(query, "q"),
                 page=_int_param(query, "page", 1, 1, 1_000_000),
@@ -649,6 +649,28 @@ def _year_param(query: Mapping[str, list[str]]) -> int | None:
     return value
 
 
+def _growth_days_param(query: Mapping[str, list[str]]) -> int | str:
+    """榜单传 1~365；首页可传 auto（由查询层按 home_growth_days 解析）。"""
+    raw = _optional_str(query, "growth_days")
+    if raw is None:
+        return 7
+    if raw == "auto":
+        return "auto"
+    try:
+        value = int(raw)
+    except ValueError as exc:
+        raise ApiError(
+            HTTPStatus.BAD_REQUEST, "bad_request",
+            "growth_days 必须是整数或 auto",
+        ) from exc
+    if value < 1 or value > 365:
+        raise ApiError(
+            HTTPStatus.BAD_REQUEST, "bad_request",
+            "growth_days 必须在 1~365 之间",
+        )
+    return value
+
+
 def _int_param(
     query: Mapping[str, list[str]],
     name: str,