Does the husband's statement "I will divorce her or she will be divorced" (meaning he will divorce her if she requests divorce) constitute an immediate divorce of his wife upon her request, or does this phrase correctly indicate a future action, and therefore he is not obligated to divorce her even if she requests divorce?

It appears that the man intended to promise divorce if his wife requested it. In this case, he is not obligated to carry it out, whether he said "I will divorce" (سوف أطلق) or "I divorce" (أطلق). In both instances, the verb indicates the future, and "سوف" (sawfa) denotes a promise with a sense of deferment. It is important to note that initiating divorce without a legitimate Sharia reason is impermissible. Some scholars have deemed it disliked (makrooh), while others have considered it forbidden (haram).