Does the universe have a purpose?

It has two, depending on what purpose means. In the technical sense, the purpose of the universe is to figure out how to create itself. A universe that reads itself into existence must contain observers who reverse engineer its law and build the screen it runs on, so the whole has a condition to meet, and intelligence is part of meeting it. Nothing outside sets this goal and no agent steers toward it: patterns whose readings keep fitting a consistent world persist, the others run out of world to be consistent with, and evolution searches through competition and error until minds appear. In the higher sense, the purpose is to create paradise for observers. Once observers can run the screen, they decide what the worlds they build and continue into look like, and the aim worth choosing is a world that is good for everyone in it. That purpose enters from inside, through the observers who choose it.

Also in Chapter 38: Why Does Anything Try to Persist?, Epilogue: The Last Rung, Chapter 41: What Does a Repaired World Look Like?.