Update sub-component batteries from parent HA entity in poller and live sync

models.py

@@ -86,6 +86,13 @@ class Device(Base):
             return sum(c.battery_slots for c in self.children)
         return self.battery_slots
 
+    def installed_batteries(self):
+        """Installed batteries on this device, including its sub-components."""
+        bats = [b for b in self.batteries if b.status == "installed"]
+        for child in self.children:
+            bats.extend(b for b in child.batteries if b.status == "installed")
+        return bats
+
     def __repr__(self):
         return f"<Device {self.name}>"