The thing to remember is this.
Efficiency isn't power consumption, its power consumption for a given workload over time, people made this mistake when they challenged Steve Burke to undervolt Intel CPU's and put them up against AMD's CPU to show they are in fact not "more efficient" Which Steve did, AMD's CPU's still did more work per watt than Intel's CPU's, this with AMD's CPU's untouched, to which Steve made the point AMD's CPU's can also be undervolted, so shut up!
The c core use less power because they don't clock as high, so less volts, but given that they also don't do the same amount of work as the standard cores.
And here is the thing about modern cores, they will only use as much power as they need for a given workload, i know the cores in my 5800X will scale anything from 0.002 watts to 12 watts, if its only doing "light background tasks" the cores will only use so much power as it needs to do that, the CPU does not need to be an older generation smaller core to save power on these light tasks, your big core will do that because they simply will not burn more power than they need to.
In fact i would argue that AMD full fat Zen 4 cores are more efficient at these tasks than Intel 14'th Gen little cores simply by virtue that they are newer more advanced cores, i can say that with confidence because no matter what workload, light work, heavy work or idle AMD's all big core Laptop's always win the battery longevity tests with the same size KW/h battery.
I repeat....