Is the wife still under her husband's authority after she refused to accompany him to Syria and he told her: "If you don't come, then you have permission to be divorced," and is it permissible for her to divorce him without sin?

It is permissible for a husband to delegate his wife to divorce herself from him. The husband's statement, "If you do not come, then you have permission to divorce," permits the wife to divorce herself unless the husband revokes this permission. The wife can divorce herself and wait for the 'iddah (waiting period) then marry another, or join her husband after coordinating with him, or be patient and not divorce herself. There is no sin upon her in choosing divorce.