We define purpose as the main point of oir life. Every perspn has a different purpose from the other. On the other hand, the purpose of living organisms is to survive. The real question is, does everything need a propose? Look at the rain as it has no purpose. It"s just a natural phenomenon. Allah SWT isn't there for a reason. He is just there for no reason because he is eternal, uncreated, uncaused. Why would the creator beg to the laws of his creation? So, yes Allah has no purpose, he may not create anytging after.us at all. It's better to not think how Allah looks like, or what he is. Such questions are pointless becuase none knows the nature of God.