Does speech that occurs in secret, such as "you are not my wife," count as a divorce by كناية (implication) and thus effect a divorce, especially with the abundance of doubts and obsessive thoughts about divorce after reading fatwas and jurisprudential books?

If the situation is as you described, then this is a whisper of divorce (waswasah) that does no harm. Do not pay attention to it, seek refuge with Allah from the accursed Shaytan, ask your Lord for well-being, and diligently maintain your adhkar (remembrances of Allah) and ruqya (Islamic exorcism/healing).