However, the story does not stop there. For a reason wholly unexplained in the text, the Rabbis decide to burn everything R' Eliezer declared pure and excommunicate him. Hijinks ensue. You can read a translation here.
I warn in advance however that part of the problem with translations is they make this look like a more coherent narrative than is supported by the text.
The first question that actually arises is "why do we find this story here?" Not, "why does it exist" but "what the heck is it doing in Baba Metziyah 59a-59b. It is unfortunately the tendency to treat the Oven of Achnai as a stand alone, utterly divorced from the surrounding text, and to close over the obvious inconsistencies in the text that occur if we treat this as a unified narrative (such as how R' Gamliel apparently teleported from the Sanhedrin in Yavneh to a boat in the middle of the ocean). It also requires us to ignore the plain language of the text which indicates multiple sources. Nevertheless, what purports to be scholarly analysis generally treats the Oven of Achnai story as a unified narrative and utterly divorced from context.
It helps to appreciate that the Gemorah, unlike the Mishna, is not the result of a single editorial vision. This does not make inclusion random. But there is a huge difference between a compilation of source material with a single editor (the Mishnah, under R' Yehuda HaNasi) and an editorial project curated over several centuries by multiple editors -- and for an entirely different purpose. The Mishna has a much more uniform view, and its stories have much greater internal coherence. (And interesting consequence of this is that we have source material, such as bereitah, which are considered valid authority despite exclusion from the Mishnah.)
My personal interpretation is that the stories around the Oven of Achnai are a debate about the difficulties of maintaining religious and institutional coherence while not resorting to excessive discipline, which can have negative consequences for the broader community as well as being hurtful to individuals. I will pause momentarily to savor the irony that the general interpretation of the non-Orthodox movements to see this as legitimizing existing authority to overrule Traditional authority, which is directly contrary to the point of the first story (value of institutional authority and national unity), whereas those who cite this for the primacy of halachic institutions completely ignore the fact that excessive discipline in the name of conformity triggers profound negative consequences.
First, here is my translation of everything after when Elijah appears to the Sanhedrin and tells them God got a good belly laugh out of their outsmarting him.
"They said that very day 'bring out all the pure things that R' Eliezer declared pure' and they burned them in fire. They voted on him and blessed him [a euphemism for placing him in charem]. And they said 'who shall go and make this known to him?' R' Akiva said to them: I will go, lest someone not appropriate should go and make it known to him and we shall find the destruction of the entire world. What did R' Akiva do? He wore black cloth and wrapped himself in black cloth then he sat before him [R' Eliezer] at a distance of over 4 cubits. Rabbi Eliezer said to him: 'R' Akiva, what is different today from other days?' He [R' Akiva] said to him [R' Eliezer]: 'My Rabbi, it appears to me that our friends have separated from you.' Then he [presumably R' Eliezer]] tore his clothes and put off his sandals, he slipped [from off his chair] and sat upon the ground, his eyes filled with tears. The world suffered/was disabled/lost a third of its olives, a third of its wheat, and a third of its barley. Some say even the dough in the hands of women swelled [spoiled]. [An unnamed source from a breitah teaches] So great was [not specified in text] that in every place that Rabbi Eliezer placed his eyes, it was burnt up.* And even [At that moment] R' Gamliel who was traveling in a boat a great wave rose up to submerse him. He said: 'It appears to me this can only be because of the matter of R' Eliezer ben Harkanus.' He stood upon his legs and said: 'Master of the World! Let it be clear and understood before you that not for my honor did I do this, nor for the honor of my father's house did I do this, but rather for your glory, that arguments shall not multiply within Israel.** The sea then rested. Aima Shalom, the wife of R' Eliezer was the sister of R' Gamliel, from the time of this incident and onward, would not permit R' Eliezer to fall upon his face [in the prayer of supplication]. It happened on the New Moon [the beginning of the month, when the supplication prayer is not said] and she was confused between an missing and a full month.*** There are those who say a poor person came at that moment and she went to bring him bread. When she returned, he [R' Eliezer] had fallen on his face [in the prayer of supplication]. She said to him: 'Rise! For you have killed my brother!" At that very moment, a cry went from the house of R' Gamliel that he rested [with his fathers, i.e., he was dead]. He [R' Eliezer] asked: 'How did you know?' [Presumably, how did you know that my prayer of supplication would kill R' Gamliel.] She said to him: 'This I have as a tradition from my father's house. All the gates are locked except the Gates of Suffering [caused by another person.]****
*This feature of a sage offended casing things to burn with his eyes is repeated in other stories involving other sages. For example, when the mystic R' Shimon Bar Yohcai emerged from his cave of exile, he was angry that people wasted time growing crops and attending to Earthly needs rather than study the Torah. Everywhere he looked, fields would burn until a voice from Heaven decreed: 'Did you come forth to destroy my world? Return to your cave!'
**This is also given as the justification for providing an Aramaic translation for the Prophets. When R' Yonaton translated the Prophets into Aramaic, (similar to the Aramaic translation of the five books of Moses by Onkelos), the Earth shook and a voice came from Heaven "Who is revealing my secrets!" R' Yonaton replied: "Not for my honor, or the honor of my house, but for your honor, to prevent arguments from multiplying in Israel."
***The Jewish month can have either 29 or 30 days. When the month was declared by witnesses, if a witness had not arrived by the 30th day, it was celebrated as a New Moon in case witnesses were in transit. If witnesses appeared the following day and testified that the New Moon had appeared the previous night, a second day of New Moon was declared.The previous day was retroactively the 30th day of the Month, and the day the witnesses testified to was the 1st day. After the calendar became fixed, the Rabbis used the mechanism of a "missing" (29 day) month and a "full" (30 day) month to control the calendar for various purposes.
****Two elements are noteworthy about this end, first, it links back to the conversation in the Gemorah that was occurring before the oven of Achnai was raised. It also closes the general topic, as the next phrase "Tanu Rabannan" [our Rabbis taught in a breitah] generally signals a change of topic or an attack question on a proposition.