I have heard it is at least theoretically possible for a Judge in criminal court in Georgia to reconsider a sentence. If a Judge is contacted by an interested person to request such a reconsideration, would the court automatically notify the (convicted) defendant? Or, is it possible to contact a criminal court Judge in a confidential manner?
Generally speaking, ex parte communications with a judge (i.e. communications to which all parties to a case are not notified) are prohibited, both by law and as a matter of judicial and attorney ethics, subject to some narrow exceptions (e.g. applications for arrest warrants prior to the arrest warrant being carried out).
Generally speaking, communications with the court (which is to say with judges or their subordinates) are made a matter of public record, and if the communication is about a particular case, all attorneys in the case must be given notice of it (if someone is not represented by an attorney, the notice goes to the defendant rather than their non-existent attorney). The attorney may then communicate the communication to their client, and generally speaking should communicate it to the client.
I don't see anything in the question that suggests that this proposed communication would fall outside the general rule. But, the question isn't very specific and I wouldn't rule out the possibility that an exception might apply in a case with very unusual facts.
Also, usually, a request to reconsider a sentence has to be made by a formal motion filed by the prosecutor or the defendant. Generally speaking, a third-party cannot file that motion unilaterally. A third-party or victim would usually only have input into the decision through the prosecutor's office. Third parties and victims are not generally permitted to file motions to reconsider sentences that have been imposed even in states with "victim's rights" statutes, but can publicly provide input to the court before a sentence is imposed, usually at the behest of either the prosecutor or the defendant.
Furthermore, generally a criminal defendant has a constitutional right to not have a sentence made more severe after being sentenced the first time around. Reconsideration of a sentence once it is imposed may only be in the direction of leniency. Once a sentence is imposed, it can't be reconsidered to be made more harsh.