Did St. John Chrysostom believe in papal papacy—i.e., that the pope has supreme power and primacy over the entire Church?
As St. Robert Bellarmine wrote in De Romano Pontifice bk. 2 ch. 15, "That the Roman Pontiff Succeeds Peter in the Ecclesiastical Monarchy is Proved from the Greek Fathers":
The seventh [proof] is [that of] St. John Chrysostom, who says in Epistle 1 to Pope Innocent:
I ask that you would write the fact that these things were done so wickedly that they have no strength, moreover that those who behaved so wickedly ought to be subjected to the penalty of Ecclesiastical laws.
Theophilus the Bishop of Alexandria had deposed Chrysostom from the Episcopate of Constantinople in a Council of many bishops. Chrysostom wrote to the Roman Pontiff, that he would discern with his authority, that the judgment of Theophilus was void, and punish Theophilus himself. Therefore, Chrysostom acknowledged Pope Innocent as a the supreme judge even of the Greeks. Likewise, in his 2nd epistle to the same:
We thank you in perpetuity, because you have declared your paternal benevolence to us, etc.
This ordeal is covered in more detail in Palladius of Aspuna's biography of St. John Chrysostom.