Is a wife forbidden to her husband if she does not inform him of the details of past situations for fear that they might be related to a previous engagement, after he stipulated that she would be forbidden to him if she lied or wronged regarding her previous engagement, and he had already forbidden her to him twice before?

The husband's statement is the decisive factor in divorce or prohibition because he knows his intention best. The more preponderant opinion is that a husband's prohibition of his wife, contingent on a condition, varies according to his intention. If he intended divorce by it, then it is a divorce. If he intended ẓihār (a form of injurious divorce by likening one's wife to an unmarriageable kin), then it is ẓihār. If he intended an oath, or did not specify anything, then it is an oath, like an oath by Allah. So, if the husband made the prohibition contingent on the wife lying and concealing relationships that are called "engagement" (irtibāṭ), then the wife is not obliged to inform him about ordinary conversations that do not rise to the level of "engagement." The wife should ignore these intrusive thoughts and seek treatment for them.