Does imagining one's wife and saying "You are absolved of me" in an internal voice constitute a kinayah (allusion) of divorce, and is intimacy with her thereafter considered a رجعة (revocation of divorce), and is it obligatory to inform her of this?

If you did not utter what crossed your mind from inner thoughts, then nothing results from it, for the Prophet, peace and blessings be upon him, said: "Indeed, Allah has forgiven my nation for whatever inner thoughts they have, as long as they do not act upon them or speak them." Divorce does not occur merely by intention. However, if you uttered the phrase "you are released from me" and you meant "release me," then divorce does not occur because the divorce of one who errs does not occur, and because Allah has forgiven the nation for mistakes and forgetfulness, and because "you are released from me" is among the ambiguous expressions (kinayat) by which divorce does not occur unless the husband intends it, and as long as you did not intend divorce, it does not occur.