Does divorce occur if I say to my wife "Go marry" when she is about to enter the bathroom, and then repeat the word "marry" out of context at a later time? And is this considered a divine punishment for excessive waswas (obsessive whispering) regarding matters of divorce, purity, and prayer?

Any utterance that implies separation but is not explicit about it is considered a kinayah (allusion) of divorce, and divorce does not occur by it unless there is an intention to effect it. The phrase "اخلصي" (get rid of me / be done with it) is not one of the kinayat of divorce. Similarly, saying "تزوجي" (marry) twice without intending divorce does not necessitate anything. And if the husband says to his wife: "اذهبي وتزوجي" (Go and marry) or "تزوجي من شئت" (Marry whomever you wish), it is not considered a divorce unless he intended divorce by it. What the questioner mentioned is not a punishment; rather, it is a form of waswasah (obsessive whispering). We advise her to abandon these obsessive thoughts and disregard them.