Y'shayahu / Isaiah 53:4 does not say anything about a healing ministry, let alone that the messiah would have a healing ministry. The passage reads: "But in truth it was our ills that he bore, and our pains that he carried -- but we had regarded him diseased, stricken by G-d and afflicted!"
Luke 6:17 - 19 speaks of Jesus healing as part of his ministry -- but this is not a messianic prophecy found in the T'nach -- and it is not found in Y'shayahu / Isaiah 53:4.
Perhaps the list maker thinks Y'shayahu / Isaiah 53:4 applies to Jesus healing people because it says that the servant bears the ills and pains of others -- but ask yourself, was Jesus ever considered to be diseased?
Was Jesus ever considered to be stricken by G-d?
Also no. The Christian bible says that G-d said: "This is my beloved Son, in whom I am well pleased" Matthew 3:17.
Remember that the speaker in Y'shayahu / Isaiah 53:3 is the gentile nations. The non-Jewish nations say that the servant "was despised and isolated from men, a man of pains and accustomed to illness. As one from whom we would hide our faces; he was despised and we had no regard for him"
It is the servant who is accustomed to illness (also not a description of Jesus) and isolated. The nations are saying that the illness they perceived the servant to have was not actually their own sickness, but the ills and pains of the gentile nations which the servant has carried.
Jesus is not described as being ill -- and so the concept that this passage could be about a healing ministry for the ills of others is not found in the Christian bible Y'shayahu / Isaiah 53:4 says "But in truth it was our ills that he bore, and our pains that he carried -- but we had regarded him diseased, stricken by G-d and afflicted!"
The messiah is never described as being ill -- but the Jewish nation is described this way in the T'nach (bible). Read Y'rmiyahu / Jeremiah 30 which speaks of the messianic age when G-d will return the Jews to the land of Israel "I will restore the captivity of My people Israel and Judah, says the Lord, and I will restore them to the land that I gave their forefathers and they shall possess it." Y'rmiyahu / Jeremiah 30:3 Read down a few lines, Jeremiah describes the Jewish people as in need of healing -- who needs healing -- the sick! "For I will bring healing to you, and of your wounds I will heal you, says the L-rd, for they called you an outcast, that is Zion whom no one seeks out." Y'rmiyahu / Jeremiah 30:17.
"For I will bring healing to you, and of your wounds" Y'rmiyahu / Jeremiah 30:17.
"a man of pains and accustomed to illness." Y'shayahu / Isaiah 53:3
"they called you an outcast, that is Zion whom no one seeks out." Y'rmiyahu / Jeremiah 30:17.
"regarded him diseased, stricken by G-d and afflicted." Y'shayahu / Isaiah 53:4
Jeremiah is echoing the words of Isaiah -- about the Jewish people. The Jews were perceived as a sick person, full of pain -- an outcast -- but the Jews carried persecution of the gentile nations -- primarily the Christian nations who exiled the Jews, isolated us in ghettos, stole our wealth and our very lives. Even today many anti-Semites will accuse the Jews of being punished by G-d for killing Jesus -- saying we have worldwide conspiracies and worse. This abuse has happened from the early days of Christianity and continue today -- including in Muslim countries who even today accuse Jews of blood libel.
Here is the Artscroll Stone Edition translation along with their footnotes at the bottom of each response to aid in your understanding of the passage.
Isaiah 52:13 Behold, My servant will succeed; he will be exalted and become high and exceedingly lofty.
14 Just as multitudes were astonished over you (saying) "His appearance is too marred to be a man's, and his visage to be human,
15 so will the many nations exclaim about him, and kings will shut their mouths (in amazement) for they will see that which had never been told to them, and will perceive things they had never heard.
53:1 Who would believe what we have heard! For whom has the arm of HaShem been revealed?
2 Formerly he grew like a sapling or like the root from arid ground; he had neither form nor grandeur; we saw him, but without such visage that we could desire him.
3 He was despised and isolated from men, a man of pains and accustomed to illness. As one from whom we would hide our faces; he was despise and we had no regard for him.
4 But in truth it was our ills that he bore, and our pains that he carried -- but we had regarded him diseased, stricken by G-d and afflicted!
5 He was pained because of our rebellious sins and oppressed through our iniquities; the chastisement upon him was for our benefit, and through his wounds we were healed.
6 We have all strayed like sheep each of us turning his own way and HaShem inflicted upon him the iniquity of us all.
7 He was persecuted and afflicted but did not open his mouth; like a sheep being led to the slaughter or a ewe that is silent before her shearers, he did not open his mouth.
8 Now that he has been released from captivity and judgment who could have imagined such a generation? For he had been removed from the land of the living, an affliction upon them that was my people's sin.
9 He submitted himself to his grave like wicked men; and the wealthy (submitted) to his executions for committing no crime and with no deceit in his mouth.
10 HaShem desired to oppress him and He afflicted him; if his soul would acknowledge guilt he would see offspring and live long days and the desire or HaShem would succeed in his hand.
11. He would see (the purpose) and be satisfied with his soul's distress. With his knowledge My servant will vindicate the Righteous One to multitudes; it is their iniquities that he will carry.
12. Therefore, I will assign him a portion from the multitudes and he will divide the mighty as spoils -- in return for having poured out his soul for death and being counted among the wicked, for he bore the sin of the multitudes, and prayed for the wicked.
Isaiah 52:13 i.e. G-d's servant the people of Israel (Rashi)
52:15 Just as Israel had once been astonishingly degraded, so it will astonish the nations by its exaltedness when the time of redemption arrives.
53:1-3 this is the prophecy foretelling what the nations and their kings will exclaim when they witness Israel's rejuvenation. The nations will contrast their former scornful attitude toward the Jews (vv. 1-3) with their new realization of Israel's grandeur (vv 4-7).
53:5 we brought suffering upon Israel for our own selfish purposes; it was not, as we had claimed, that G-d was punishing Israel for its own evil behavior.
53:6 We sinned by inflicting punishment upon Israel. Such oppression is often described as "Hashem's punishment" (see 10:5, Habakkuk 1:12), for He decreed that it should happen (Abarbanel).
53:8 When Israel's exile is finally ended the nations will marvel that such a generation could have survived the expulsion from "the land of the living, i.e. Israel, that the nations had sinfully inflicted upon it.
53:9 Ordinary Jews chose to die like common criminals, rather than renounce their faith; and wealthy Jews were killed for no reason other than to enable their wicked conquerors to confiscate their riches (Radak).
53:10 That is, Israel. G-d replies to the nations that Israel's suffering was a punishment for its own sins; and when the people realize this and repent, they will be redeemed and rewarded.
53:11 Israel will teach the nations of G-d's righteousness.