Thanks for the great question! One interesting phenomenon that really matches the idea of the canary is that of “early warning signals”: basically, mathematical theory predicts that a system that’s about to cross a tipping point will start fluctuating more slowly, and this can be measured. There is a lot of work going into assessing elements of the climate system that might have tipping points, and searching for such early warning signals: one recent example is the Atlantic Meridional Overturning Circulation (AMOC; think Gulf stream). Recent work (e.g. Boers 2021) suggests that the AMOC is currently exhibiting early warning signals for collapse.

With respect to the global-scale disruption events, we could say that the canary is the historical record itself. Appropriately analyzed, the record suggests that there is a critical rate of CO2 perturbation at which mass extinction occurs, and that we are on track to cross the threshold by 2100 (see also this comment). Nevertheless, since it may take thousands of years for the ultimate consequences to play out, actions we take today to mitigate this could still have an effect.