One of the biggest challenges with climate change is that it continually increases variance in the system as warming increases. It's hard enough to correctly model a stable climate system, but modeling one that will be continuously changing for many human lifetimes is very hard.
We're not headed to a "new normal", if we ('we' being life on this planet and human civilization) were we'd simply adapt to it, it would be costly, but survivable.
But climate change will continue to cause radical and increasingly difficult to predict changes, and those changes themselves are subject to equally radical future transitions. This is why climate change is such a true crisis: it cannot be "adapted" to, because there is no stationary state we'll arrive at any time soon.
Just look at Europe: the last few years it's been experience extreme heatwaves, but if the AMOC collapses (which it may, even in our life time) that will likely cause it to experience extreme cold. Even then the exact details of an event as extreme as the AMOC collapsing are hard to predict, and the AMOC collapsing is just one of countless other similarly extreme events we are going to be facing in coming decades.