Correct. But Paul did not go there to establish his authority or to learn for himself the correct answer.
Acts 15:2
they determined that Paul and Barnabas, and certain other of them, should go up to Jerusalem unto the apostles and elders about this question.
At the conclusion of the Jerusalem council they sent men of their own along with Paul and Barnabas with letters of the official word, these men were Barsabas and Silas, chief men among the brethren:
Paul leaves all of this out in his own writings in Galatians.
Agreed. I think it is perhaps that both the accounts in Acts and Galatians reflect how Paul’s authority as an apostle was constantly being challenged. He had to make his case repeatedly. In Acts the believers were not willing to allow his authority as an apostle to settle the matter. In Galatians he does not feel the need to recount his subordinate role in this council in Jerusalem. Today, Paul’s authority as an apostle in unquestioned by pretty much anyone who identifies as “Christian”. During his ministry though, it was another story.
Paul goes further to assert his BETTER understanding of the Gospel for the Gentiles, describing himself as the apostle to the Gentiles. He also asserts that he labored more than any other apostle and was not inferior in any way to the other apostles, even Peter. He demonstrates his authority in recounting the need for him to publicly reprove Peter.