It is possible to translate “prosopos” as “presence” (an example of that is 2 Cor 10:1) and of course the direct meaning is “face”, nearly always synonymous with “person”. But in the case of 2 Cor 2:10 “presence” makes no sense because St. Paul makes a reference to his authority stemming from the authority of Christ. What he is saying is that he absolves the penitent in agreement with the decision of the local church and on authority of Christ. As St. John Chrysostom explain, he absolves him not in order to please the local priests but because that is the right thing to do, in Christ.
But there is no hint that Paul was discussing authority in any way, the context and the words he used do not point to such an interpretation against the established literal meaning and usage of “face” or “presence” for “prosopos”.
Furthermore you misunderstand what Chrysostom said:
Your comment was, “As St. John Chrysostom explain, he absolves him not in order to please the local priests but because that is the right thing to do, in Christ.”
But Chrysostom indicates just that, that Paul was simply trying to avoid producing hurt feeling because of some feeling overlooked.
Chrysostom:
“Then lest they should be hurt, as though overlooked, he adds, “for your sakes.” What then? Did he for men's sake pardon? No; for on this account he added, “In the person of Christ.”
And he asks, “What then? Did he for men's sake pardon?” and answers “No” even though that is exactly what Paul said he DID do! “..for your sakes forgave I it”.
But Chrysostom adds: “for on this account he added, “In the person of Christ.” which could indicate he thought Paul was imitating Christ in being forgiving.
But even here there is no discussion of Paul's authority to forgive or simply because “that is the right thing to do”.