The court might also accept projects to adapt to climate change as „climate action“, but to my knowledge such projects are pursued even less than reducing emissions (for good reason).

That's not at all what this is about.

Climate immutability is not a human right, but if something is shown to cause harm, then you might reasonably expect humanity to limit this harm.

Also in my mind when talking about developing and middle-income nations what level of prosperity is human right? And what level of emissions resulting in climate change is acceptable? As surely denying prosperity is more against human rights than delaying climate change...