If you go to you tube, and run a search for “fulton sheen and prayer” a talk comes up where he answers this toward the end of part two. Here’s the short version.
Us worshiping God is like a little girl picking flowers and giving them to her mother. Does the mother need the flowers? No, the mother doesn’t need them. Does the child need to give them? Of course. The child has been given a home, been cared for, loved etc. For her to not give the flowers would mean that she would be lacking in affection and love and gratitude. Similarly, God does not need our worship for his own sake. We need it, ie, we need to give it. We have been given life, Jesus etc and for us to not give worship would mean that we would be lacking in affection, love, and gratitude.
So, God does not demand our worship for his own sake, any more than the mother needs the flowers. But the mother still values the flowers as an expression of her daughter’s love and gratitude. Similarly, God does not need our worship (He has no needs), but he does value it as an expression of our love and gratitude. And more, being love himself, he values wants us to come to know him and so values our worship in that it brings us closer to him. So God does not need our love, we do, but he still values it.