As I was quite happy, that I almost solved this challenge exactly like the solution I still wonder: why is there a need for the actionButtonUIList? All available buttons are already in actionButtonContainerTransform.
My UpdateSelectedVisual() looks like this:
private void UpdateSelectedVisual()
{
foreach(Transform buttonTransform in actionButtonContainerTransform)
{
ActionButtonUI actionButtonUI = buttonTransform.GetComponent<ActionButtonUI>();
actionButtonUI.UpdateSelectedVisual();
}
}