Is saying, "I wish I had not formalized the marriage, and there had been a divorce," with the intention of getting rid of obsessive thoughts, considered an implicit divorce, given that the speaker was alone and not with his wife?

Divorce pronounced by a person suffering from obsessive-compulsive disorder (waswas) like yourself does not take effect, even if he explicitly uttered the word of divorce, let alone if he used a كناية (allusive term). This is even more true if he did not utter it with the intention of initiating a divorce. What came to your mind or what you uttered as a wish for divorce is not the divorce itself, for wishing for something is not the thing itself. One of the best ways to treat obsessive thoughts is to ignore them and to anger Satan by not paying attention to them.