Egg is a much harder thing to replace. My son is vegan so my wife is often baking things that are vegan. Chia egg or aquafaba are usually pretty good. She makes a vegan muffin that I honestly prefer to “normal” muffins. Although I’m not 100% sure what she puts in them, I’d bet its applesauce.

Whatever you do, don’t ever have vegan “cheesecake”…. run away… quickly