Does divorce take place by saying, "Each of us goes our own way," with the intention of divorce, given that the speaker did not know that divorce occurs through allusive phrases, and intended to delay an explicit divorce?

As long as you did not intend to effect a divorce with that phrase, then no divorce has occurred, because it is an ambiguous expression (kinayah) and was not accompanied by intent. You are not bound by anything due to your future intention to divorce. We advise you not to rush into divorcing your wife, but rather to be patient with her, strive to improve her, and look at her good qualities, in accordance with the Almighty's saying: "And live with them in kindness. For if you dislike them - perhaps you dislike a thing and Allah makes therein much good" (Quran 4:19), and the Prophet's (peace be upon him) saying: "Let no believing man hate a believing woman; if he dislikes one of her characteristics, he will be pleased with another." If life between you cannot be reconciled, then there is no blame upon you for divorcing her, but this should be the last resort.