What is visible in the graphs are trendlines, which are converted into CO2 sensitivity by a calculation that is not motivated.

The big hangup about climate sensitivity has never been much about the  sensitivity of purely CO2 - which is something that can be calculated and measured in lab conditions (it's about 1 degree for doubled CO2). The issue always has been about the effects of feedbacks, positive and negative, to increasing atmospheric CO2, in addition to the higher forcing of increased CO2.

Hansen, and Schmidt, assign certain weights to certain forcings based on certain estimates and certain model runs to explain the observed trendline, thereby finding a certain sensitivity.

There's mathematics involved, but it is far from being all hard.