The issue is DropdownMenu was expecting an Icon not IconButton.

trailingIcon: IconButton(
  icon: const Icon(Icons.clear),
  onPressed: () {
    controller.clear();
  },
),

Can be replaced with

trailingIcon: InkWell(
  child: const Icon(Icons.clear),
  onTap: () {
    controller.clear();
  },
),