PAY ATTENTION.
In Acts 22 there, Paul was recounting his first return to Jerusalem after his conversion.
Paul was sent far hence unto the Gentiles early on.
Now see an overview of the when and where.
Acts 26:20
But shewed first unto them of Damascus, and at Jerusalem, and throughout all the coasts of Judaea, and then to the Gentiles, that they should repent and turn to God, and do works meet for repentance.
We can now determine when Paul and Barnabas first turned to the alien Gentiles.
It was during their first journey outside the coasts of Judea.
The place was at Antioch in Pisidia.(not Antioch,Syria)
Acts 13 verse 14...
But when they departed from Perga, they came to Antioch in Pisidia, and went into the synagogue on the sabbath day, and sat down.
The when....
The next week about 30,000 alien Gentiles showed up.
44 And the next sabbath day came almost the whole city together to hear the word of God.
45 But when the Jews saw the multitudes, they were filled with envy, and spake against those things which were spoken by Paul, contradicting and blaspheming.
Acts 13:46
Then Paul and Barnabas waxed bold, and said, It was necessary that the word of God should first have been spoken to you: but seeing ye put it from you, and judge yourselves unworthy of everlasting life, lo, we turn to the Gentiles.
"PAY ATTENTION"
Your claim is that "Paul was sent far hence unto the Gentiles early on" (these are the far hence Gentiles as in aliens and strangers Ephesians 2:11-12 KJV) and that "Now we see an overview of the when and where" and go on to quote Acts 26:20. Let's take a look at more of Acts 26 in the King James Bible to tell us what time it really is, what sending of Paul Acts 26 is giving account to and to whom!
Acts 26:13 At midday, O king, I saw in the way a light from heaven, above the brightness of the sun, shining round about me and them which journeyed with me.
Acts 26:14 And when we were all fallen to the earth, I heard a voice speaking unto me, and saying in the Hebrew tongue, Saul, Saul, why persecutest thou me? it is hard for thee to kick against the pricks.
Acts 26:15 And I said, Who art thou, Lord? And he said, I am Jesus whom thou persecutest.
Acts 26:16 But rise, and stand upon thy feet: for I have appeared unto thee for this purpose, to make thee a minister and a witness both of these things which thou hast seen, and of those things in the which I will appear unto thee;
Acts 26:17 Delivering thee from the people, and from the Gentiles, unto whom now I send thee,
Acts 26:18 To open their eyes, and to turn them from darkness to light, and from the power of Satan unto God, that they may receive forgiveness of sins, and inheritance among them which are sanctified by faith that is in me.
Acts 26:19 Whereupon, O king Agrippa, I was not disobedient unto the heavenly vision:
Acts 26:20 But shewed first unto them of Damascus, and at Jerusalem, and throughout all the coasts of Judaea, and then to the Gentiles, that they should repent and turn to God, and do works meet for repentance.
The above is the testimony of Paul to King Agrippa written by Luke. It is another account of the first appearing of the Lord Jesus Christ to the apostle Paul (then Saul) in Acts 9:1-7 KJV. The Lord tells Paul for what purpose He appeared unto him, "to make thee a minister and a witness both of these things which thou hast seen" and a promise of a later appearing "and of those things in the which I will appear unto thee;". Paul's testimony of what the Lord told him does not stop there, but continues on to give us even more conclusive evidence of the immediate sending of Paul (then Saul) with, "Delivering thee from the people, and from the Gentiles, unto whom now I send thee,". "Now I send thee" means exactly that: "NOW"! Verse 20 finishes it off with a "shewed first unto them...". This is, without a doubt, an Acts 9 sending/ a straightway" sending from Acts 9:20 KJV. The Acts 13 citing you gave also fits the first sending, location (synagogue) and audience to whom salvation was sent then Acts 13:16 KJV, Acts 13:26 KJV.
That is neither the second sending of Paul when he revealed the temple vision (Acts 22:17-21 KJV) which happened much later (Acts 18:21-22 KJV fourth journey) nor were the alien Gentiles (Ephesians 2:11-12 KJV) the same as those he was first sent to during Acts (Galatians 3:29 KJV). The temple vision reveals the second sending of Paul, "I will send thee" (Acts 22:21 KJV) while the first sending was "now I send thee" (Acts 26:17 KJV).
That should get your attention to 2 Timothy 2:15 KJV!