Add support for custom weekly backup schedule (#136079)

* Add support for custom weekly backup schedule

* Rename the new flag to custom_days

* Make the store change backwards compatible

* Improve comments

homeassistant/components/backup/websocket.py

@@ -8,7 +8,7 @@ from homeassistant.components import websocket_api
 from homeassistant.core import HomeAssistant, callback
 from homeassistant.helpers import config_validation as cv
 
-from .config import ScheduleState
+from .config import Day, ScheduleRecurrence
 from .const import DATA_MANAGER, LOGGER
 from .manager import (
     DecryptOnDowloadNotSupported,
@@ -320,13 +320,17 @@ async def handle_config_info(
 ) -> None:
     """Send the stored backup config."""
     manager = hass.data[DATA_MANAGER]
+    config = manager.config.data.to_dict()
+    # Remove state from schedule, it's not needed in the frontend
+    # mypy doesn't like deleting from TypedDict, ignore it
+    del config["schedule"]["state"]  # type: ignore[misc]
     connection.send_result(
         msg["id"],
         {
-            "config": manager.config.data.to_dict()
+            "config": config
             | {
                 "next_automatic_backup": manager.config.data.schedule.next_automatic_backup
-            },
+            }
         },
     )
 
@@ -358,7 +362,12 @@ async def handle_config_info(
         ),
         vol.Optional("schedule"): vol.Schema(
             {
-                vol.Optional("state"): vol.All(str, vol.Coerce(ScheduleState)),
+                vol.Optional("days"): vol.Any(
+                    vol.All([vol.Coerce(Day)], vol.Unique()),
+                ),
+                vol.Optional("recurrence"): vol.All(
+                    str, vol.Coerce(ScheduleRecurrence)
+                ),
                 vol.Optional("time"): vol.Any(cv.time, None),
             }
         ),