Am I required to do anything to pass the Miqat, given that the Amir has undertaken to slaughter the sacrificial animal?

If you passed the Miqat intending to perform the ritual and you entered into a state of ihram after passing it, a compensatory sacrifice (dam) becomes obligatory upon you, to be slaughtered in Mecca and distributed among the poor of the Haram. If you are unable to do so, you must fast for ten days. Your obligation is not discharged until you are certain that the expiation (fidyah) has been performed. If you know that it has been discharged on your behalf, that suffices you according to many jurists. However, if you discharge it yourself, that is more cautious. Otherwise, you are obligated to perform it.