Does ẓihār occur if a husband says to his wife, "You are to me as the back [ẓahr] of," and does not complete the last word, or completes it with the name of an animal, or completes it with a forbidden word in the context of jest or doubt, and does a four-month fast then become obligatory?

What happened between the spouses over the phone is not considered ẓihār, because the wording was not uttered to establish it, but rather to recount. As for what occurred in jest, ẓihār does not result from it as long as the husband is not certain that he uttered an explicit ẓihār formula, especially if the husband is prone to excessive waswasah (whispers/doubts). And a man's statement to his wife, "You are to me like the back of a donkey," is most likely not ẓihār; some say it is ẓihār if he intended it as such.