What is the ruling on the following two situations: The husband saying to his wife, "We won't work out together," in an unconfirmed voice (whether it was voiced or not), and then repeating the same phrase several times at the end of the day with the intention of asking about its ruling?

Merely recounting a divorce without the intention of initiating it does not necessitate anything. The aforementioned utterance in the question does not constitute a divorce because there was no intention of initiating it, and because the wording is neither explicit nor an allusion to divorce. The one afflicted by waswas (obsessive whispering) should disregard these whispers, seek refuge in Allah from them, and frequently recite the Qur'an and engage in dhikr (remembrance of Allah), bearing in mind that inner speech does not constitute a divorce.