No, they're almost entirely unrelated. Almost all CPUs will idle close to 0 W (with correctly working drivers). The main idle power contribution comes from the mainboard and other devices (e.g. disks). The Mini PCs you mentioned should have a very low total idle power, probably below 10W.
Check out Wolfgang on YouTube, he has some great videos on the topic: https://youtu.be/Ppo6C_JhDHM
I think when I messed it up, it worked when I tried switching to the proprietary drivers for the second time. I think you can try that without much risk.
In my case I ended up disabling Secure Boot anyway because it just got too annoying (a BIOS update breaking it was the final straw for me). The security benefit after you've enrolled a MOK seems dubious anyway. It would be nice if distros could ship signed kernels with the open-source Nvidia driver but I guess that's not happening.