Does divorce occur with the words "she is divorced" spoken audibly to oneself, with the intention of not completing the marriage, without an addressee or the wife's knowledge?

Your informing your wife of your unwillingness to continue the marriage is considered a divorce if you intended separation by it. However, if you did not intend divorce, then it is considered nothing, because allusive (kinaya) expressions do not constitute divorce unless the intention is concurrent with the utterance.

If you utter a clear divorce statement verbally, then the divorce occurs. But if it is merely an internal monologue without verbalization, then nothing results from it.

In the event that a divorce occurs by kinaya with intention, or by a spoken utterance, before consummation with the wife and before intimacy, it is considered an irrevocable (bain) divorce, and she cannot be taken back except with a new contract, a new Mahr (dowry), witnesses, and the guardian's consent, based on the Almighty's saying: "O you who have believed, when you marry believing women and then divorce them before you have touched them, then there is not for you any 'iddah (definition) to count concerning them. So provide for them and release them with a gracious release." {Al-Ahzab: 49}.