Cheating done properly
If AI grades essays, then AI must be used to generate essays. Only peers can grade proportionally. When AI and humans grade equally, then the singularity is upon us and we humans are no longer of any use anyway.
Therefore, when AI is used used to grade, then the only possible correct way to deal with it would be to have our dear good students generate their essays with AI. Then, all will have good grades and the ministry of education statistics will finally be perfect. That is a commendable goal for the policy makers.
Do not teach our students how to be creative. Simply teach them how to push a button. It is much more (cost) effective to generate educated button-pushers than to have thinking people. All hail to the future button pushers. The next step is to replace both teachers and students. The AI can and will produce its own perfect score. No human intervention required. All hail to AI; may the human race be replaced by a perfectly sane and rational alternative.