Is uttering "By God" considered an oath, even if one restrains oneself from completing the rest of the oath that came to mind as a self-dialogue without vocalizing it, especially given that I used to suffer from obsessive doubts concerning divorce?

As long as you have not uttered the object of the oath, your oath is not binding. Indeed, intention without utterance does not constitute an oath or a divorce. Divorce does not occur except by utterance. So, if one intends it in his heart without uttering it, it does not occur according to the majority of scholars.