Must female congregants who sat for the first Tashahhud when the Imam stood for the third rak‘ah inadvertently repeat the Dhuhr prayer, given that they then followed the Imam and completed the prayer with him?

It appears that your prayers are valid, and your falling behind the Imam in standing for the third rak'ah out of ignorance does not invalidate it. This is because falling behind the Imam by two pillars due to an excuse does not invalidate the prayer. You are also correct in following the Imam in the prostration of forgetfulness for omitting the first Tashahhud (definition).