Desecrating Shabbat for the purpose of pain relief

There are poskim who believe that it is forbidden to even violate Shabbat in order to save a person from losing a limb. Only real pikuach nefesh rejects Shabbat. There are also doubters and even some reject it, but that is only about real pikuach nefesh. Rabbis distort the halakha without any evidence from the Talmud or the poskim.
One could perhaps believe that this was also said about mental illness, but certainly not about pain relief, especially since there are medications that can be taken instead.

In a few more years, this ruling will be used to allow more problematic things. Some of the Orthodox are not much different from the Reforms. The difference may only be in the pace of changes, perhaps

Where the danger to one's limb leads to the danger of life, everyone permits it. The Talmudic claim that in the event of the danger to one's limb it is forbidden to desecrate the Sabbath is a statement of principle and not necessarily a practical teaching. There is no change here necessarily from the Talmudic intention, just as Amoraic interpretations of the Mishnah or Baraita are valid (see my article on the Okinoth).
Regarding the attitude towards change and reform, you have a fundamental lack of understanding on the matter. See my articles on idolatry ‘enlightened’ and more, and in detail in the sixth chapter of the third book in the trilogy.

Instead of danger, is it not because of the risk of losing a limb? There are also quite a few jurists who have literally forbidden violating Shabbat in order to save a limb.

I answered that.