Thank you for quoting scripture. Now let's compare it to your original claim:
Galatians 2:7-9 reads:
But on the contrary, seeing that I had been entrusted with the gospel to the uncircumcised, just as Peter had been to the circumcised (for He who was at work for Peter in his apostleship to the circumcised was at work for me also to the Gentiles), and recognizing the grace that had been given to me, James and Cephas and John, who were reputed to be pillars, gave to me and Barnabas the right hand of fellowship, so that we might go to the Gentiles, and they to the circumcised.
There is nothing here specifically putting those words in the mouth of Peter.
It is not even clear that Peter was present when Paul first came to meet some of the apostles in Jerusalem. Moreover, Paul AND Barnabas were sent "to the Gentiles," not solely, Paul.
So your primary claim of Paul being the only apostle to the Gentiles is wrong, based on the scriptural evidence you cited. We have no idea what Peter said here, but I think it is safe to assume that he approved of Paul going to the Gentiles, especially since Peter was the first to take the gospel to them himself (Acts 10).
And if you are familiar with Acts, you will know that Paul's practice when entering a new city was to go find the synagogue and first present the gospel to them. So Paul definitely took the gospel to the circumcised, and it was frequent enough that he circumcised Timothy (Acts 16:3) so that it would not be a stumbling block to the Jews to which he ministered.