The commission of Matthew 28 was not a revelation to go to Gentiles.
The commission of Mark 16 was not a revelation to go to Gentiles.
The commission of Luke 24 was not a revealtion to go to Gentiles.
The commission of Acts 1:8 was not a revelation to go to Gentiles.
The “commission,” if you will, to Peter to go to Cornelius’ house was consistant with Old Testmanet prophesy that as Israel is blessed, the Gentiles too would be brought in under that blessing, but was not a revelation to go to Gentiles in general. Peter still later agreed with Paul to confine his ministry to the circumcision (Galatians 2).
Prior to the Cross everything was directed to Israel. The Jewish perspective was based on their Tanak(?) our OT. They were looking for a warrior Messiah who would establish His Kingdom on Earth. No one understood that a spiritual kingdom bringing in Gentiles was going to be done first.
What we are talking about in Acts is the difference in The Gospel between Peter and Paul. I'm saying that on close review they aren't different. Peter is talking to a Jewish only audience and Paul was led to the Gentiles, but both are preaching salvation by Faith Alone in Christ Alone.
Acts 2:38 Then Peter said to them, "Repent, and let everyone of you be baptized in the name of Jesus Christ for the remission of sins; and you shall receive the gift of the Holy Spirit.
Repentance for the Jews would be recognizing Jesus Christ for who He is and believing in Him. How would this differ from recognizing that Jesus died for our sins and by believing in Him we are saved?
Also, the word Repent stands alone. It is to be done before baptism. The baptism is following an act of Faith Alone and the baptism is declaring it is Jesus Christ who has remitted your sins not the water.