The prayers weren’t a part of it, but they were required at the end. It was written and added to the required Leonine Prayers in 1886 by Pope Leo XIII. so, yes, while it wasn’t part of the Mass per se, they were required prayers upon ceasing the liturgical part.
They were dropped from the NO, which caused a great deal of distress to the people. They are considered suppressed and part of the TLM, and thus not supposed to be attached to the end of the NO and led by the priest (Cupich said laypeople could recite it privately).
In some dioceses, however, the bishop has actually permitted their resroration at the end of NO masses. But technically, they’re not supposed to be led by the priest, and that’s what Cupich used as his excuse.
Again, that is not true. If it was, the prayers would also have been recited after High Masses prior to VC II.
The Oath against Modernism, required of all priests, was also never part of the Mass; yet Montini rescinded it in 1967. He cleaned the slate for the New Springtime, the New Pentecost, et al.