There are halakhic decisors who hold that it is forbidden even to desecrate the Sabbath in order to save a person from losing a limb. Only actual danger to life overrides the Sabbath. Doubt does too, and even multiple doubts, but that is only when it is truly a matter of danger to life. Rabbis are distorting Jewish law without any proof from the Talmud or the halakhic decisors.
Perhaps one could argue that this was also said about mental illness, but certainly not about pain relief, especially when there are medications that can be taken instead.

A few more years and people will use this ruling to permit other problematic things. Some Orthodox are not all that different from the Reform movement. Maybe the only difference is just the pace of the changes.

In a case where danger to a limb will lead to danger to life, everyone permits it. The Talmudic claim that in danger to a limb one may not desecrate the Sabbath is a principled statement and not necessarily a practical ruling. There is not necessarily any change here from the Talmud’s intent, just as amoraic interpretations of a Mishnah or baraita formulate contextual readings; see my article on such contextual reinterpretations.
As for your attitude toward change and Reform, you have a fundamental misunderstanding of the matter. See my articles on “Enlightened” idolatry and more, and in detail in the sixth section of the third book of the trilogy.

In a case of danger, is it not because of danger to life, and not because of danger of losing a limb? There are also quite a few halakhic decisors who explicitly forbade desecrating the Sabbath in order to save a limb.

I already answered that.