Is the woman in question considered a wife or a divorcee, knowing that her husband verbally took her back after the second divorce, and his intention in doing so was to divorce her for the third time to deprive her of her rights?

If a man divorces his wife for the second time and then takes her back with the intention of harming her by prolonging her waiting period (iddah), he has violated Allah’s command: (and do not hold them back, intending harm, so that you transgress). If the husband takes her back after the second divorce, she is legally his wife. If he then divorces her a third time, the divorce takes effect, and a major separation (baynunah kubra) occurs. Upon the third divorce, the divorcée is not entitled to maintenance (nafaqah) or dwelling (sukna), unless she is pregnant, based on the Prophet's (peace be upon him) statement to Fatimah bint Qays: "You have no right to maintenance or dwelling," and in another narration: "unless you are pregnant."