The passage in Sanhedrin 98b,can't be taken as one of the claimed proofs that in the Jewish tradition ,exits an individual messianic interpretation,of Isaiah 53.
from Wikipedia "Isaiah 53":
"Sanhedrin 98b in the Babylonian Talmud speculates rather ironically about the undisclosed name of the unrevealed Jewish Messiah to come, so as to say it could be anyone: leper of the school (a hint on rabbinical disciples cast out of their seminary/school) based on Isaiah 53:4, Rabbi Nachman based on Jeremiah 30:21, Shiloh based on Genesis 49:10, Yinon based on Psalm 72:17, Rabbi Hanina reckons it is him, based on Jeremiah 16:13, Menachem ben Hizkija based on Lamentations 1:16"
quote from steinsaltz.org
Sanhedrin 98a-b: Candidates for Messiah
"The Gemara on today’s daf continues its discussion of mashi’aḥ – the Messiah. One of the questions that is dealt with is “What is his name?” Several possibilities are suggested in the Gemara –
In Rabbi Sheila’s study hall the suggestion was “Shiloh” (see Bereshit 49:10)
In Rabbi Yannai’s study hall the suggestion was “Yinnon” (see Tehillim 72:17)
In Rabbi Ḥanina’s study hall the suggestion was “Ḥanina” (see Yirmiyahu 16:13)
Another suggestion raised was that he is “Menaḥem ben Ḥizkiyya” (see Eikha 1:16).
Clearly all of these Sages were suggesting the names of their teachers as potential candidates to be the Messiah – something that we find regarding the names of other Sages in different midrashim, as well. This is, apparently, based on the continuation of the Gemara where it is taught that in every generation there are individuals who are worthy of being the Messiah, but because the time has not yet come he cannot be crowned as such. The students sitting in the various study halls each saw their own Rabbi as being the one most likely to play that role in that generation.
The Gra suggests that the names listed in the Gemara form an acrostic –
whose opening letters spell out “Mashi’aḥ.”
Rav Naḥman is quoted as saying that if the Messiah was someone who was living in his generation, then he – Rav Naḥman himself – would be the obvious candidate. The passage that he refers to in order to support his claim appears in Sefer Yirmiyahu (30:21) where we learn that it is someone already in a leadership position who will be the mashi’aḥ, and Rav Naḥman filled that role.
Even in later generations it was not uncommon to find Jewish leaders who hinted in their writings to the possibility that they were worthy of bringing the redemption, something that was, on occasion, taken very seriously by their students. "
The "leper scholar" was a real Jew and he is mentioned a few times in Talmud. Marguliout HaYom a commentary on the Talmud by Rabbi Reuven Margolious (an Israeli Talmudic scholar and head of the Rambam Library at Tel Aviv University) wrote: “Look at the Jerusalem Talmud Tractate Chagigah chapter 2 Halacha 1. There we see that Rabbi had a special wise student who taught on the ‘Work of the Chariot’, without the approval of Rabbi, and for that he was stricken with leprosy. This talmid who was stricken was called ‘the leper of the house of Rabbi.’ And they said about him, ‘Surely our diseases he did bear’”
The QUOTES of the schools mentioned, were being driven by the names of their beloved rabbis, and presented names for the messiah based on plays on the names of their own teachers ....
while it is true that they extracted some of the names from verses that previously were interpreted as messianic ,but that doesn't necessarily require, that it was the case with all the names .
for example the case of Jer 16:13 ,nowhere in the Jewish literature that it has been interpreted messianicaly at all.
and the only instance outside the Talmud to Isaiah 53 ,that has a messianic reference ,is found in The Targum of Jonathan ben Uzziel
What is abundantly clear is that the targum very clearly portrays the messiah as a conquering warrior, not as a suffering servant. The targum’s interpretation of Isaiah radically alters Isaiah’s meaning. In the targum, it is not the messiah who suffers; the messiah conquers. Rather, it is the messiah’s enemies, and the nation of Israel, who suffer.
to conclude the point : when the rabbis said : "The leper of the house of Rabbi Yehuda HaNasi is his name, as it is stated: “Indeed our illnesses he did bear and our pains he endured; yet we did esteem him injured, stricken by God, and afflicted” (Isaiah 53:4)."
they were reading the life of this beloved master (whom they thought to deserve to be the messiah of his generation) into a passage of Isaiah 53 ,out of its context ..
to say :"our beloved Yehuda HaNasi the messiah of this generation, though some may think that he was stricken by God, and afflicted "being a leper",yet the contrary is true ...
It is in some way similar to the case of early Christians, who read the crucifixion into a passage (Isaiah 53) that has never been read as "a suffering, dying messiah ben David) before Christianity.
the new testament affirms repeatedly that the idea of a suffering ,dying messiah ben David, was a new one (shocking even to the followers of Jesus),let alone the rest of the Jews (a stumbling block for the Jews) see (1 Corinthians 1:23) etc....