Please explain further as I am not sure what error Peter recognized. In the story of Paul’s conversion, it is to Ananais that the Lord reveals Paul’s mission. We do not hear Paul speak of this special mission until later.
The whole story seems to indicate that Paul was converted by Jesus, and then Paul was accepted by the others, a form of imprimatur. He preaches for a time in Damascus, but then seems to go on a sabbatical of sorts for three years. After that time, he returns and spends 15 days with Peter after which he begins his ministry.
Paul sets himself apart from the others yet claims that they accept him and his reception of the Gospel. So, he sees his mission as different than theirs, but still teaches that the Gospel he received is the same as that of the others.
Now, if we pay close attention to the Gospel, we hear Jesus tell them to go out to ALL the world making them disciples and baptizing them. So the word ALL would seem to include Gentiles.
So, it is a bit complicated, but we have God giving the initial reception of Gentiles to Peter, who then brings it to the council in Jerusalem and then Paul declaring himself the Apostle to the Gentiles in Galatians.
Just FYI.
Acts 26
Paul Tells of His Conversion
12"In this connection I journeyed to Damascus with the authority and commission of the chief priests. 13At midday, O king, I saw on the way a light from heaven, brighter than the sun, that shone around me and those who journeyed with me. 14And when we had all fallen to the ground, I heard a voice saying to me in the Hebrew language, 'Saul, Saul, why are you persecuting me? It is hard for you to kick against the goads.' 15And I said, 'Who are you, Lord?' And the Lord said, 'I am Jesus whom you are persecuting. 16But rise and stand upon your feet, for I have appeared to you for this purpose, to appoint you as a servant and witness to the things in which you have seen me and to those in which I will appear to you, 17 delivering you from your people and from the Gentiles— to whom I am sending you 18 to open their eyes, so that they may turn from darkness to light and from the power of Satan to God, that they may receive forgiveness of sins and a place among those who are sanctified by faith in me.'
19"Therefore, O King Agrippa, I was not disobedient to the heavenly vision, 20but declared first to those in Damascus, then in Jerusalem and throughout all the region of Judea, and also to the Gentiles, that they should repent and turn to God, performing deeds in keeping with their repentance. 21For this reason the Jews seized me in the temple and tried to kill me.