Does divorce occur if the wife stops praying, given that the husband told her: "I will not live with someone who doesn't pray," and he did not intend to initiate a new divorce?

You have done well by showing concern about your wife's neglect of prayer. It is best to approach her with good counsel and teach her, and you should be wary of using divorce to solve such problems. Your statement to your wife, "I will not live with someone who does not pray," is an implicit promise of divorce that does not constitute a divorce, nor is it obligatory to fulfill it, especially since you doubt your intention, and the default is not to intend divorce. We alert you to the seriousness of neglecting prayer, as it is the second pillar of Islam, and some scholars have even considered the one who abandons it to be a disbeliever.