the framework in which Jewish law eternally binding and unchanging…aka Judaism.
Jewish law has never been unchanging. Even going back to pre-rabbinic Judaism, we can see changes in the law within the Torah. For example:
2 If you buy a Hebrew slave, he shall work for six years, and in the seventh he shall go free, without payment. 3 If he came by himself, he shall go out by himself; if he had a wife, his wife shall go with him. 4 If his master gave him a wife, and she bore him sons or daughters, the wife and her children shall belong to her master [i.e., the slave-owner], and he [the slave] shall go by himself. 5 And if the slave sincerely says, "I love my master and my wife and my children; I don't wish to go free," 6 then his master shall bring him before God [i.e., a temple; or perhaps, "before judges"--i.e., to a court of law], and he will bring him to the door or the doorpost. His master shall then pierce his ear with an awl; and he [the slave] will work for him [the master] forever. 7 If a man sells his daughter to be a slave, she shall not go free as a male slave goes free. [There follows a separate set of laws, according to which a female slave may not request freedom, but may be set free if her master dislikes her; she may not be sold to an outsider.]
12 If your brother, a Hebrew, is sold to you, whether a male or a female, he will work for you for six years. In the seventh year, you shall set him free. 13 And when you set him free, you shall not send him away empty-handed. 14 Be sure to apportion to him some of what comes from your flock and your threshing floor and your wine-vat. You shall give to him that with which God had blessed you. 15 You should remember that you were a slave in the land of Egypt, and God rescued you. Therefore I command you this thing today. 16 But if he says to you, "I do not wish to go away from you," because he loves you and your house and enjoys being with you, 17 then you shall take the awl and put it through his ear into the door; and he will be your slave forever. You shall also do this for your female slave. 18 Do not let yourself feel severe when you set him free: for six years he worked for you twice as hard as a hired man would have. HaShem your God will bless you in all you do.
It's very clear that the passage from Deuteronomy is referencing the older law from Exodus: both passages concern treatment of a fellow Hebrew slave, and both are centered on the core idea of working for six years and freedom on the seventh, with the option to forego that freedom if desired. Perhaps most crucially, both contain the ritual of piercing the ear with an awl at the doorpost in the case that a slave wishes to remain. That's very specific; it certainly didn't evolve independently twice within Israelite culture. The Deuteronomic author was almost certainly reading a copy of the law from Exodus; at the very least, they were familiar with the ideas it contained.
And they make changes to it. The law now applies to both men and women. One can no longer release a slave directly into poverty, you have to free them with the materials to restart their life. It is no longer stated that a freed slave must leave his wife and children behind if he married during enslavement, and the fact that women must also be freed allows room for the implication that the whole family should be allowed to go together. Deuteronomy introduced the idea that there can only be one temple in one set location, so Exodus's assumption that one could easily get to a temple no longer holds. The ritual of piercing the ear with an awl is thus adapted to take place at the doorpost of one's own home, where being "before God" can now be represented through the mezuzah.
Besides the concrete changes in law, there's also a dramatic shift in perspective and tone. The Exodus law clearly favors the slaveowner. In the very first sentence, the slaveowner is the subject, who is buying the slave. The law is built in such a way as to increase the odds that a slave will "want" to stay. By being freed with nothing and returning to his farm after 6 whole years away, he will need to immediately take on debt to get the seed and possibly equipment to start farming again--and of course, debt is probably what brought him into slavery in the first place, so there's a very real risk that he'll stay in that cycle and end up enslaved again anyway. All after being separated from his family! By contrast, Deuteronomy favors the slave. In the first sentence, the slave is the subject, and he is referred to as your brother, forcing the reader to foreground his experience as important. By being freed with the materials to restart his life, and likely having his family with him, he is much less likely to choose to stay as the "less bad" option. It's much more humane.
But the Deuteronomic author faces a challenge: everyone is already following the Exodus law, and if slaveowners are acting in their own economic self-interest, they'll probably prefer the old version. So Deuteronomy attempts to persuade, not merely state the law. The author repeats that the law now also applies to women, placing emphasis and ensuring that the earlier "male or female" cannot be written off as a scribal error. They reassure the slaveowner that they still benefited from slavery, and that God will bless them for following this version of the law. They refer to the slave as "your brother" and invoke the Israelite's founding myth of having been enslaved in Egypt, providing reasoning for the change.
And this kind of thing has shown up again and again in Jewish law for millennia. The Mishnah is unusual in the way it only states the law--and it's not long until the Gemara steps in to add that reasoning. When you read a teshuvah, it doesn't just contain the ruling the rabbis settled on. It includes their reasoning and cites the precedents they're drawing on.
The details of what changed in the laws of slavery between Exodus and Deuteronomy aren't the important part here. Honestly, I probably got a little carried away elaborating on that. The important part is that Jewish law has always been open to change and reinterpretation, even going back as far as when parts of the Torah were still being written. Moving forward in time a bit, the entire premise of Rabbinic Judaism is "how do we adapt our laws to fit our current situation?" The first "current situation" that needed adapting to was, of course, no longer having a temple. But that was far from the last. Today's rabbis adapting halakhah to things like electricity and the internet and modern medicine are engaging in the same process as the earliest rabbis adapting halakhah to the destruction of the temple and living in exile. Today's rabbis asserting egalitarianism, asserting that women can read from the Torah and lead services and become rabbis, are engaging in the same process as the author of Deuteronomy amending the laws in Exodus to free a female slave as well as a male one.
