Does Catholic Church acknowledge St. Paul the Apostle as consecrated Bishop during Apostolic times?
The answer is YES, if we accept the number of Popes who had chosen the name of St.Paul as their papal name.
Pope Paul I (757–767)
Pope Paul II (1464–1471)
Pope Paul III (1534–1549)
Pope Paul IV (1555–1559)
Pope Paul V (1605–1621)
Pope Paul VI (1963–1978)
St.Pope Paul VI is perhaps the most well known to had witnessed the charism of St.Paul the Apostles as a Missionary Bishops preaching the gospel of Christ to many parts of the world.
Paul VI, an 'evangelical' pope
For Francis, the key to Paul's pontificate was his 1975 exhortation on evangelization, Evangelii Nuntiandi ("On Proclaiming the Gospel"), which Francis has called "the greatest pastoral document written to date."
In that landmark document -- largely overshadowed by the contraception encyclical -- Paul said that the church itself "has a constant need of being evangelized," and he wrote that people today listen "more willingly to witnesses than to teachers," so Catholic leaders above all must practice what they preach.
"The world calls for, and expects from us, simplicity of life, the spirit of prayer, charity towards all, especially towards the lowly and the poor, obedience and humility, detachment and self-sacrifice. Without this mark of holiness, our word will have difficulty in touching the heart of modern man. It risks being vain and sterile," Paul wrote in words that could have come from the pen of Francis.
In fact, in November 2013, Francis sent a personal representative to a meeting of the U.S. bishops and had him read those passages to the hierarchy, followed by clear instructions that Francis, like Paul, "wants 'pastoral' bishops, not bishops who profess or follow a particular ideology." Francis also asked all eight cardinals in his special advisory groups to reread Evangelii Nuntiandi.
https://www.ncronline.org/news/people/pope-paul-vi-almost-saint-here-are-four-his-biggest-legacies
After St.Pope Paul VI, the next two Popes had chosen to combine the name of St.Paul the Apostle with St.John the beloved apostle.
Pope John Paul I (1978)
Pope John Paul II (1978–2005)
The Church also celebrates the feast day celebration of St.Peter and St.Pau the Apostle;
The Feast of Saints Peter and Paul or Solemnity of Saints Peter and Paul is a liturgical feast in honour of the martyrdom in Rome of the apostles Saint Peter and Saint Paul, which is observed on 29 June. The celebration is of ancient origin, the date selected being the anniversary of either their death or the translation of their relics.[2]
https://en.wikipedia.org/wiki/Feast_of_Saints_Peter_and_Paul
But, to answer the question on hand;
Does Catholic Church acknowledge St. Paul the Apostle as consecrated Bishop during Apostolic times?
Biblical Proof that St.Paul the Apostle can confer the Sacrament of Confirmation which is proper only to Bishop can be seen in the following passages;
Acts 19:6 New International Version (NIV)
6 When Paul placed his hands on them, the Holy Spirit came on them, and they spoke in tongues[a] and prophesied.
This can be seen as the same effect on the people who had experienced the Pentecost.
Acts 2 New International Version (NIV)
The Holy Spirit Comes at Pentecost
2 When the day of Pentecost came, they were all together in one place. 2 Suddenly a sound like the blowing of a violent wind came from heaven and filled the whole house where they were sitting. 3 They saw what seemed to be tongues of fire that separated and came to rest on each of them. 4 All of them were filled with the Holy Spirit and began to speak in other tongues[a] as the Spirit enabled them.
The remaining question is, when did St.Paul received the "anointing" as Bishop?
Is the laying of hands of Ananias "enough to consecrate" St.Paul as Bishop?
So Ananias went to the house, and when he arrived, he placed his hands on Saul. “Brother Saul,” he said, “the Lord Jesus, who appeared to you on the road as you were coming here, has sent me so that you may see again and be filled with the Holy Spirit.” (Acts9:17)
Is the laying of hands of Anannias has the power to confer raising Saul to episcopate or Bishop or Prince of the Church?
So, where can we found the biblical passage pertaining to Saul consecration as Bishop?
The answer is in Acts13:1-2;
Acts 13 New International Version (NIV)
13 1 Now in the church at Antioch there were prophets and teachers: Barnabas, Simeon called Niger, Lucius of Cyrene, Manaen (who had been brought up with Herod the tetrarch) and Saul. 2 While they were worshiping the Lord and fasting, the Holy Spirit said, “Set apart for me Barnabas and Saul for the work to which I have called them.” 3 So after they had fasted and prayed, they placed their hands on them and sent them off.
Now, these passage has "prophets" plus they "united in praying thru worship and fasting" resembling the Mary and the Apostles as they invoke the Holy Spirit to come down. Also, since the prophets knew the Jewish Tradition in "anointing with oils" if one will be "set aside for a mission meaning chosen" to empower them with the Holy Spirit, did the prophet "anoint Saul & Barnabas with oils" like what prophet Samuel did to Saul and David that made them Prince of Israel or Bishop?
We can see on the next passages it mentioned the name of Saul became Paul and mentioned that he was "filled by the Holy Spirit", not only that it display the power of Saul now name Paul to exorcise demons which in the Catholic Church reserve only to the Bishop.
They traveled through the whole island until they came to Paphos. There they met a Jewish sorcerer and false prophet named Bar-Jesus, 7 who was an attendant of the proconsul, Sergius Paulus. The proconsul, an intelligent man, sent for Barnabas and Saul because he wanted to hear the word of God. 8 But Elymas the sorcerer (for that is what his name means) opposed them and tried to turn the proconsul from the faith. 9 Then Saul, who was also called Paul, filled with the Holy Spirit, looked straight at Elymas and said, 10 “You are a child of the devil and an enemy of everything that is right! You are full of all kinds of deceit and trickery. Will you never stop perverting the right ways of the Lord? 11 Now the hand of the Lord is against you. You are going to be blind for a time, not even able to see the light of the sun.”
Immediately mist and darkness came over him, and he groped about, seeking someone to lead him by the hand. 12 When the proconsul saw what had happened, he believed, for he was amazed at the teaching about the Lord. (Acts13:6-12)
This passages, although not explicit stated the Holy Spirit instructed the prophet to "set aside or consecrate" and aided by united prayers of the prophets and teachers Saul & Barnabas was "filled by the Holy Spirit" and have now the power over demons and Saul name was now mentioned as Paul. A change in the character and power implied Saul becoming Paul marks his missionary role as Prince of the Gentiles a Bishop and Apostles chosen by Christ and anointed by the Holy Spirit.