Is there anything incumbent upon us for having performed ‘Umrah without entering into a state of Ihrām from the Mīqāt of Dhul-Ḥulayfah, knowing that we entered into Ihrām from the fast-track migration road, which is parallel to the Mīqāt of Al-Juḥfah? And is our ‘Umrah valid?

Your 'Umrah (definition) is valid, but it was obligatory to enter into a state of ihram (definition) from the place where you formed the intention for 'Umrah, and not when you were parallel to Al-Juhfah. This is based on the Prophet's (peace be upon him) saying: "And whoever is less than that (meaning, lives within the miqat (definition) boundaries), then from where he initiates." Therefore, delaying the ihram beyond the place where you intended 'Umrah necessitates sacrificing an animal (dam) and distributing its meat to the poor of the Haram (definition).