Merge branch 'bluetooth_proxy_fixes' into integration

esphome/components/bluetooth_proxy/bluetooth_proxy.cpp

@@ -159,11 +159,6 @@ void BluetoothProxy::loop() {
     return;
   }
 
-  // Early return if no advertisements pending
-  if (this->advertisement_count_ == 0) {
-    return;
-  }
-
   // Flush any pending BLE advertisements that have been accumulated but not yet sent
   uint32_t now = App.get_loop_component_start_time();