The monotheistic all powerful one.
But then the answer to if he can do anything would be a no, since he can’t pick up the rock
The question boils down to can an omnipotent being give up his omnipotence. The answer is yes. When he gives up his omnipotence there is no paradox to him no-longer being able to pick up a rock.
Not even that. Omnipotence means that you can both make something impossible for yourself and still be able to do it. Paradoxes have nothing on omnipotence.
I don’t like that definition because it makes the word meaningless. Omnipotence means all powerful (with in the reference of the speaker, or whatever constraints of the word “power” the speaker is using.) If omnipotence is incomprehensible, then maybe we should invent a different word to convey that idea, perhaps “Godly”. As it is, omnipotence as a word has value in the English language that is distinct from God. Same with Omniscience, or any of the other Omni’s.