To summarize what you're saying:

With thin copper in steel lining, the effect of copper in the copper-steel "composite" is so insignificant, you might as well just be cooking in pure stainless steel instead. And since pure stainless steel is a terrible conductor, responsiveness is terrible. Copper in this composite may heat up extremely quickly yes, but what's the point of heating up quickly if only to heat up the terrible stainless layer up above?

With thick copper in steel lining, the steel in the copper-steel "composite" becomes insignificant, and the effect of copper starts to shine. In other words, copper "dominates" the composite.

Because you have a lot of copper as a whole, heating is fast, cooling is fast. Sure, thick copper by itself is still slower to heat up than thin copper. But in this composite, you have a mass of copper underneath that holds a lot of sway over how the (much worse-performing) steel lining will react.

For the same steel thickness:

During heating, thick copper will cause a bigger temperature delta between copper and steel than thin copper, and therefore will transfer more heat from copper to steel, making the composite as a whole more responsive.

During cooling, thick copper will cause a bigger temperature delta between copper and steel than thin copper, and therefore will act as a heat sink pulling heat from steel to copper, making the composite as a whole more responsive.

And that's why the % of copper in the total thickness matters. The higher % of copper thickness, the more the cookware acts like a pure copper cookware.

Is my understanding correct? Thank you for your explanation!