Same here. MacBook Pro 16", i7, Catalina, CPU usage of Resolve when idle between 20 and 30%. FCPX in comparison 0 - 5%.
This is an issue when on the road and running on the internal battery. There should be no reason to drain the battery while no intensive activity is going on.
btw. a few more observations:
while QuickTime player was running a video Resolve's cpu load fell by 10%
Also after a few hours of work including adding audio plugins and color grading CPU load in idle state went up by 10% averaging between 30-40% (even after restarting the program).
And when the Fairlight page is open Resolve needs roughly another 10% in idle state, bringing it up to 50% in total.