Does the third divorce take place if the husband says to his wife: "If you commit adultery, then you are thrice divorced," and she then engages in foreplay without penetration?

The majority of scholars hold that a conditional divorce takes effect if the condition it was tied to occurs, and this is the fatwa given. If, by conditioning the divorce on zina (fornication/adultery), you meant only zina that incurs the hadd (prescribed punishment), then the divorce has not occurred as long as she has not committed it. However, if you meant zina and its مقدمات (preludes/ مقدمات), then it has occurred. Your wife erred by informing you of what she fell into, and you erred by making the divorce conditional. A man is obligated to be the guardian of his wife, to close the doors to fitan (trials/temptations), and to uphold the boundaries of Allah. It is not a condition for the validity of repentance to declare sins; rather, concealing them is what is required.