> how it’s presented in public discourse

My problem is that this article is not helping in this regard.

Not exactly. Increases in average temperature are very easy to measure, [0] for a nice visualization.

The change was done to highlight the fact that the consequences are not just higher temperatures but also include, for example, an increased frequency in wild fires, droughts, and other extreme weather events.

[0]: https://climate.nasa.gov/climate_resources/300/video-climate...

No. It was 'rebranded' because you have senators bringing in snowballs as a claim that global warming didn't exist because the common avenue for denying global warming is to point to the current weather.

CO2 levels are current 1.50 times pre-industrial levels, so "previous doubling" is misleading.

It's not the saturation at the peak absorbtion frequencies that is driving the warming, it's the widening of the curves which raises absorbtion levels in nearby frequencies. The "saturated" argument was one of the first objections when the science was poorly understood. Krauss's book Physics of Climate CHange has a good account of this history. Check IPCC summaries to see how many models from the literature predict flattening at 0.7C additional warming if we don't curb emissions (spoiler alert: slim to none with many positing 5C or more additional warming in the 2100's if emissions aren't curbed).