It’s clear that climate change has at best a small probability (well under 10%) of causing human extinction, but many proponents of working on other x-risks like nuclear war and AI safety would probably give low probabilities of human extinction for those risks as well. I think the positive feedback scenarios you mention (permafrost, wetlands, and ocean hydrates) deserve some attention from an x-risk perspective because they seem to be poorly understood, so the upper bound on how severe they might be may be very high. You cite one simulation that burning all available fossil fuels would increase temperatures by 10 °C, but that isn’t necessarily an upper bound because there are non-fossil fuel sources carbon on Earth that could be released to the atmosphere. It would of course also be necessary to estimate how high the extinction risk conditional on various levels of extreme warming (8°C, 10°C, 15°C, 20°C?) would be.
Regardless, it’s a good idea to have a clear view of how big the risk is. You’re right that the casual claims about extinction or planetary uninhabitability I hear from many people who are concerned about climate change are not justified, and they seem a bit irresponsible.