After Joseph was accused of seducing Potiphar's wife, why was he sentenced to jail (for over 2 years) rather than executed?

After enraging Potiphar, Joseph was sent to jail. The Torah doesn't specify how long the term was for, but seeing as he was released 2 years after interpreting the baker's dream, it is safe to assume he was sentenced to many years in prison.

However, I was reading that the concept of long prison sentences as a punishment is a modern idea. So what was the Egyptian rationale of the prison sentence?

An important thing to note is that the article you linked is specifically referring to Western prisons, while Egypt is in the east. Furthermore, as proof for the claim in the article, a certain foreword from a particular volume of the journal Social Justice is linked, but this article does not actually say what the author of the first article is claiming (and, though I haven't gone through everything yet, it's not clear that this is written in the rest of that particular volume, either).

However, it's true that in Early Antiquity there weren't very many jails (notably, the Torah hardly ever clearly mentions imprisonment as a form of punishment). But we do have evidence that Ancient Egypt employed jails, by way of Papyrus Brooklyn 35.1446, which includes mention of a prison facility called "ḫnrt-wr" (Great Prison/Labor Camp). The same institution, or institution-type was also frequently mentioned in the better-known Admonitions of Ipuwer (AKA the Ipuwer Papyrus). These sources indicate that prisoners resided in the ḫnrt facilities and were used for forced labor, so it would seem that the rationale behind imprisoning Joseph for an extended period was for including him in the work force.1 Of course, we also know that he quickly rose through the ranks, eventually becoming some kind of foreman. Evidently he remained a prison foreman for the duration of his sentence.

1 For more information on the ḫnrt and other sources that reference it, see here, pp. 64-91.

According to tables in "Sequence of Events in the Old Testament" by Eliezer Shulman, Yosef spent in prison a total of 12 years, one of which was together with Chief Cupbearer and CHief Baker (According to Seder Olam Rabba 2:2).

Rabbi Yisroel Cohen in the book "Mitzrayim, Midrash and Myth" discusses these and related questions. First, why Yosef was not executed, but placed in jail, is explained by several commentaries, as the book notes in chapter 3 discussing uniqueness of Egyptian exile and what Jewish people learned there. Targum Yonasan Bereshis 39:20:

And Joseph's master took counsel of the priests, who ____ put him not to death, but delivered him into the house of the bound, where the king's prisoners were bound; and he was there in the house of the bound.

Also 47:22

Only the land of the priests he bought not because they had considered him innocent at the time when his master was seeking to put him to death, and they had delivered him from the judgment of death: and besides he had said that a portion should be given them from Pharoh. So they ate the portion which Pharoh gave them, and sold not their land.

Chizkuni there explains:

רק אדמת הכהנים, “only the soil belonging to the priests (Joseph did not transfer to Pharaoh).” The priests are the like the ministers, as the כהן מדין the priest of Midyan. Joseph did not transfer (land of the priests) to Pharaoh so they would not have any reason to start a rebellion against Pharaoh. A different reason given for Joseph’s preferential treatment of the priests is as we explained already, that the priests had suggested a method by which to test if Joseph or the wife of Potiphar had spoken the truth, as a result of which, Joseph instead of being hanged had only been put in jail.

The chapter 6 which brings details on how Egyptians viewed Yosef also explains what Yosef did in Egyptian jail and why was he successful there as we learn from Bereshis 39:20-22

So Joseph’s master had him put in prison (בֵּ֣ית הַסֹּ֔הַר), where the king’s prisoners were confined. and he remained there in prison. Hashem was with Joseph—He extended loving-kindness to him and He disposed the chief jailer favorably toward him. The chief jailer put in Joseph’s charge all the prisoners who were in that prison, and he was the one to carry out everything that was done there.

Ibn Ezra on Bereshis 39:21 writes:

PRISON. We can not ascertain whether bet ha-sohar (the prison) is a Hebrew or Egyptian word in view of the fact that the Bible goes on to explain its meaning (Were it a Hebrew word there would be no reason to explain the *place where the King’s prisoners were bound) as it does with the Persian word ha-achashteranim (that were used in the King’s service) which is followed by the Hebrew bene ha-rammakhim (bred of the stud) (According to I.E. bene ha-rammakhim is Hebrew for achashteranim). (Est. 8:10).

The correct Hebrew word for prison is משמר. Thus, it was an Egyptian-style jail, bet ha-sohar. To undertand what Yosef did in that jail, a hint is given in Midrash Tehilim 86:3:

"For You, Lord, are good and forgiving." Rabbi Pinchas HaKohen said that a scale is tipped here with sins on one side and merits on the other. What does the Holy One, blessed be He, do? He takes one note of debt and immediately puts it on the side of merit, as it is said, "And He extended loving-kindness to him" (Genesis 39:21).

In other words, by being in jail Egyptian prisoners were supposed to examine their deeds and repent. Therefore, as Yosef was successful there, he was helping other prisoners to do that. In fact, the book gives Shach on the Torah by Mordekhai haKohen of Tzfas" on Bereshis 39:20-22:

ויתן שר בת הסהר ביד יוסף את כל האסורים וכו' ואת כל אשר היו עושים שם הוא היה עושה, מלמד שלמדם ייחודו של הקב"ה והיו מיחדים כמוהו, ולזה אמר שר המשקים את חטאי אני מזכיר היום, למד מיוסף שהיה מתודה על חטאיו ואומר להם לא עביד דינא בלא דינא.

So Joseph’s master had him put in prison etc., and he was the one to carry out everything that was done there. It is teaching that [Yosef] taught the prisoners unity of HKBH, and they would associate their sins in accordance with the judgement of one G-d. And that that is what the Chief Cupbearer says, Bereshis 41:9, "I must make mention today of my offenses...". He learned from Yosef, who confessed his sins and said that he did not do anything against the law.

The book presents citations from Egyptian mythology to make a compelling case, that Yosef indeed helped prisoners confess their sins as in Egyptian mythology only a repentant could be guaranteed life after death. The polytheistic belief makes it hard for people to repent as different gods suggest different permitted and forbidden actions. Since this is a Judaic forum, I am referring to the book by R' Yisrael Cohen, who studied extensively ancient Egypt, review the evidence on Egyptian side.