The first point to realize is that there are multiple meanings to every word in natural language, not just one.
The second is to realize that a definition of God, is a claim about the world, and that claim is testable, and refutable. And one of the most powerful tests, and refutations, in philosophy, is to show logical contradictions.
The definition "God can do anything" leads to contradictions. The most well known is "can God make a rock too heavy for Him to lift?". Either "yes" or "No" leads to a refutation of the claim in the definition.
"God can do anything" isn't "bad", it is FALSE.
Falsified claims about our world can be patched. That is what Peter Geach tried to do, with his proposed different definition of God. What his definition does, is assume that logic is prior to God, and cannot be violated by God. So God is all powerful, within the limits of logic.
This definition too has problems. It assumes there is a One True Logic to the universe. But logicians don't think that is true. They think there are multiple logics, and different logics apply to different parts of our world. https://www.cambridge.org/core/journals/think/article/abs/guide-to-logical-pluralism-for-nonlogicians/EDFDFA1C9EB65DB71848DABD6B12D877 So the assumption in this definition by Peter Geach is false as well.
An alternate definition could be that God is sufficiently powerful to have created this universe. Our universe is not infinite, so God need not be, for God to be a creator of everything. This alternate definition also gets one out of the problems with infinities that mess up the "God can do anything" definition, and also the problems which plural logic provides for "God can do anything except for what logic prohibits". And fits the bill for what monotheists need a Creator God to do.
Three prior questions on this subject include potentially useful answers as well:
Can strong omnipotence be decomposed into logically possible and logically impossible aspects?
Problems with the Omnipotence paradox
Can someone explain omnipotence to me?