Ok well let me tell you what Christians have believed about omnipotence, essentially the bases of these beliefs cam from an old monk about 900ish years ago called anslem. Ever heard of the onotological arguement? That anslem. So he was the first one who first really thought of the perfect people or "the being that is the greatest that be conceived." ( I think that's how he put it.)
So anyway he defined the who possess omnipotence as being the source of all power (the only reason strength exists or that u have strength is because God imbues strength into creation, if I want I can go into more depth than this but maybe it would be better to make that another discussion if so) it also means that he can do everything that is logically possible. The reason why can only do the logically possible is because the Christian god is the god of order, and he imbues that order into creation ( it's why things pretty much are able to exist). It's also very important for the Christian god to be like this because in the nature of Christianity god is relational, however if god could do the logically impossible he would become impossible to have a relationship with. E.g. the Bible could be true but every word of it a lie, god could be omnibenelovent and omnimalevolent etc.
I agree that he would only be able do do what is logically possible. Let me add a caveat though: There is a distinction between doing what is logically impossible and doing what is contrary to common sense.
Using the cake example: It is contrary to common sense to able to create a cake out of thin air, but not logically impossible. It might even violate the laws of physics, but not the laws of logic. Creating a cake that happens to not be a cake, in the same sense of the word, is what would count as logically impossible.