What is the ruling regarding the action of a wife who sought Khulʻ from her husband, then married a man with whom she had been speaking on the phone a year before and after the divorce?

If a wife seeks divorce or khul' without a valid reason, she has committed a religiously forbidden act, for the Prophet, peace and blessings be upon him, said: "Any woman who asks her husband for a divorce without any compelling reason, the scent of Paradise will be forbidden to her." And if someone corrupted her against you and incited her to seek divorce, he has committed a great sin, for the Prophet, peace and blessings be upon him, said: "He who instigates a woman against her husband or a slave against his master is not one of us."

Since she has divorced and married another, you should not preoccupy yourself with her. Instead, focus on what benefits you and your children in matters of this world and the hereafter.