According to Catholicism, are Popes expected to receive power by the Holy Spirit to operate in the miraculous as Peter did? The Bible records many instances where Peter operated in the supernatural by the power of the Holy Spirit. For example:
Peter was among the disciples that were filled with the Holy Spirit at Pentecost:

When the day of Pentecost had come, they were all together in one place. 2 And suddenly a noise like a violent rushing wind came from heaven, and it filled the whole house where they were sitting. 3 And tongues that looked like fire appeared to them, distributing themselves, and a tongue rested on each one of them. 4 And they were all filled with the Holy Spirit and began to speak with different tongues, as the Spirit was giving them the ability to speak out. [Acts 2:1-4 NASB]

Peter received words of knowledge from the Holy Spirit:

But a man named Ananias, with his wife Sapphira, sold a piece of property, 2 and kept back some of the proceeds for himself, with his wife’s full knowledge, and bringing a portion of it, he laid it at the apostles’ feet. 3 But Peter said, “Ananias, why has Satan filled your heart to lie to the Holy Spirit and to keep back some of the proceeds of the land? 4 While it remained unsold, did it not remain your own? And after it was sold, was it not under your control? Why is it that you have conceived this deed in your heart? You have not lied to men, but to God.”

Peter had the power to heal the sick with his shadow:

14 And increasingly believers in the Lord, large numbers of men and women, were being added to their number, 15 to such an extent that they even carried the sick out into the streets and laid them on cots and pallets, so that when Peter came by at least his shadow might fall on any of them. 16 The people from the cities in the vicinity of Jerusalem were coming together as well, bringing people who were sick or tormented with unclean spirits, and they were all being healed. [Acts 5:14-16 NASB]

Peter had the authority to lay hands on new believers so they may receive the Holy Spirit:

14 Now when the apostles in Jerusalem heard that Samaria had received the word of God, they sent them Peter and John, 15 who came down and prayed for them that they would receive the Holy Spirit. 16 (For He had not yet fallen upon any of them; they had simply been baptized in the name of the Lord Jesus.) 17 Then they began laying their hands on them, and they were receiving the Holy Spirit. [Acts 8:14-17 NASB]

Peter had supernatural visions:

9 On the next day, as they were on their way and approaching the city, Peter went up on the housetop about the sixth hour to pray. 10 But he became hungry and wanted to eat; but while they were making preparations, he fell into a trance; 11 and he saw the sky opened up, and an object like a great sheet coming down, lowered by four corners to the ground, 12 and on it were all kinds of four-footed animals and crawling creatures of the earth and birds of the sky. 13 A voice came to him, “Get up, Peter, kill and eat!” 14 But Peter said, “By no means, Lord, for I have never eaten anything unholy and unclean.” 15 Again a voice came to him a second time, “What God has cleansed, no longer consider unholy.” 16 This happened three times, and immediately the object was taken up into the sky. [Acts 10:9-16 NASB]

Peter heard direct instructions from the voice of the Holy Spirit:

19 While Peter was reflecting on the vision, the Spirit said to him, “Behold, three men are looking for you. 20 But get up, go downstairs and accompany them without misgivings, for I have sent them Myself.” [Acts 10:19-20 NASB]


According to Catholicism, are Popes expected to be empowered by the Holy Spirit to operate in the miraculous during their ministry, just like Peter (the first Pope) did?
According to Catholicism, are Popes expected to receive power by the Holy Spirit to operate in the miraculous as Peter did?
The short answer is no.
However, if one is asking in reference to the administration of the sacraments then the answer is yes. I believe the OP is asking more so as in miraculous events having taken place.
Historically there have been popes that were saints, while others who were sinners. The Holy Spirit can chose whom he desires to operate the miraculous.
The Church has been given the gift of infallibility by the Holy Spirit when the pope pronounces on doctrine ”ex cathedra” on the points of faith and morals.
The Holy Spirit is free to chose whomever he desires to for doing his Divine Will. Caiaphas prophesied about Christ’s death, yet I do not believe many hold him as particularly worthy of working the miraculous.

49 But one of them, named Caiphas, being the high priest that year, said to them: You know nothing.
50 Neither do you consider that it is expedient for you that one man should die for the people, and that the whole nation perish not.
51 And this he spoke not of himself: but being the high priest of that year, he prophesied that Jesus should die for the nation. - John 11:49-51

Generally speaking working the miraculous goes hand in hand with one’s particular holiness, than with the office of the papacy. Even then, the real saints of God do not like to advertise such gifts given to them from the Holy Spirit. Even pope’s should strive to remain humble. The gifts they may receive in this life as pope are for the benefit of the Church and not their personal glory.
There are always a **Ridleys Believe It or Not moments in everything. Nevertheless, occasionally the miraculous has happened in the lives of some popes:

Pope Fabian I
Miracle: Was made pope when a dove landed on his head
Fabian was a layman—a Roman soldier—but when he attended the synod that was meeting, in the year 236, to elect a new pope, a dove flew into the room and landed on his head, a miraculous sign that this otherwise unknown man should be elected the next pope.
Pope Urban I
Miracle: Knocked down an idol that killed 22 people
Towards the end of his life, in 230, Urban and his followers had been imprisoned and brought before an idol, to pray. Instead, Urban prayed to the Christian God, and the idol fell down, killing 22 priests.
Pope Pius V
Miracle: Beat the Ottomans, and knew it
In October of 1571, the Vatican, along with its European allies, went into battle against the Ottoman navy, which was aiming to take over more of the continent, starting with Italy. The Pope led prayers for Christian victory—and when the European forces did triumph, he announced it before the news had returned from the battlefield.
Pope Alexander I
Miracle: Escaped a well-guarded prison cell
Early in the second century A.D., after Alexander had converted a Roman governor, Hermes, and his 1,500 person household, the emperor sent an official to investigate. The official put Alexander in jail and Hermes in the custody of another high-ranking official, Quirinus. Hermes asserted that Alexander could escape jail, with the help of Jesus Christ, and Quirinus accepted the challenge, doubling the guard. When he came back, Alexander was in the same room with Hermes.
Agapetus I
Miracle: Made a paralyzed man walk
In the early 6th century, a paralyzed man was brought to pope; after Mass, the pope took the man by the hand, and he was able to stand up.
John XXIII
Miracle: Cured a dying 23-year-old nun
In 1966, an Italian nun was on the verge of death, from a gastric hemorrhage, when another nun took a relic of the recently deceased pope and put it on the stomach of her suffering sister. Within days, the director of the hospital says, she saw Pope John in a vision and the suffering nun’s condition disappeared.
John Paul II
Miracle: Cured Parkinson’s and a brain aneurysm
Pope John Paul II died in 2005 of Parkinson’s, and three months later, Sister Marie Simon Pierre, who suffered from the same disease, prayed to him; one day, she woke up able to move again. Later, doctors told a woman in Costa Rica, Floribeth Mora Diaz, that she would die within days, of a brain aneurysm; she prayed to the pope, heard his voice tell her not to be afraid, and was healed, with no medical explanation.
Pope Celestine V
Miracle: Sheer number (7 dubious miracles, 11 real ones)
Celestine V, a monk and hermit, was pope for just five months of 1294, before abdicating the office. In his 1313 canonization hearing, a panel considered 18 miracles; they only approved 11. One allegedly miraculous cure might have actually been a medical success; others had too few or contradictory witness. Still, 11 miracles isn’t bad.
Pope Pius X
Miracle: Cured a paralyzed child, etc.
After Pius X became pope in 1903, he was credited with many healing miracles. He returned a man’s paralyzed arm to life and cured an Irish girl covered with sores. His sock cured another girl’s foot disease. A nun with abdominal cancer was cured after she swallowed a bit of his clothing. Another was curid of a hip disease after one of her young students asked the pope to pray for her.  He blessed two ailing nuns who were so restored that the driver who took them to see the pope didn’t believe they were the same people when they came out.  One of his most dramatic healing miracles, though, was curing a child who had been paralyzed since birth. He sat on the pope’s lap and within a few minutes started running around the room.
Pope Cornelius I
Miracle: His statue blessed the marriage of an unlikely couple
In medieval Germany, a lord’s daughter fell in love with an artist hired to decorate a chapel dedicated to Cornelius, a third-century pope. The lord said he would not give his blessing to the marriage unless the pope did; a devotional statue of Cornelius bowed from the altar and blessed the couple.
Pope Gregory II
Miracle: Made Christian soldiers immune to Muslim enemies
In 720, when the Duke of Aquitaine was heading into battle against a Muslim army, he fed his soldiers bits of three pieces of bread that Pope Gregory II had blessed, and everyone who ate that bread survived the battle with a wound.
Pope Clement I
Miracle: Underwater tomb revealed by ebbing sea
After he was martyred and thrown into the Black Sea in 101 A.D., the waters of the sea receded until they revealed a marble tomb, where Clement’s body was found in a stone coffin. Every year after, once a year, the sea would recede and reveal the shrine.
12 Papal Miracles: An Unscientific Ranking

&quot;Peter had the authority to lay hands on new believers so they may receive the Holy Spirit&quot;. The Popes have this same ability also along with many others within the Catholic Church when administrating the sacraments of ordination and confirmation.
Both bishops and popes lay their hands on ordinands and confirmands so they can receive  the Holy Spirit as in Acts 8:14-17.

14 Now when the apostles, who were in Jerusalem, had heard that Samaria had received the word of God, they sent unto them Peter and John.
15 Who, when they were come, prayed for them, that they might receive the Holy Ghost.
16 For he was not as yet come upon any of them; but they were only baptized in the name of the Lord Jesus.
17 Then they laid their hands upon them, and they received the Holy Ghost. - Acts 8:14-17