How should schools create an AI academic integrity policy?

Define your rules more clearly. Rules are weak when they state "No AI" because the use of AI for everything from having ideas to checking grammar has become commonplace for most students. A strong policy will define where to encourage the use of AI, where to limit the use of AI, and where to completely ban the use of AI for each type of assignment, class level, so no one is unsure as to which tools to use.
Create a clear disclosure process so that students cite AI usage in the same way they would cite a source. Establish a consistent detection workflow using a trusted detection tool, so that each detected case is reviewed in the same way.
Since models and tools developed with AI are rapidly changing, even if you had a strong policy on AI today, the models and tools will continue to improve and therefore require you to update your policy at least once every year.