Same here with Windows 10 (2004). This is just crazy.
Seems like any game controller plugged in causes this. Disabling GeForce overlay doesn't fix it. The only thing that allows the computer to sleep (or screen saver to start) is unplugging the controllers.
For reference: I have Thrustmaster Warthog HOTAS and Saitek Pro Flight Combat Rudder Pedals. If either/all of them are plugged in, my PC will never become "idle" and allow screensaver/ or sleep.
I've tried everything in this thread and others. I have updated Windows, updated drivers, updated BIOS, changed BIOS settings, changed Windows power settings (USB, etc), reset power plans, disabled "Allow wake from sleep" on all devices, and more. The only thing that works is unplugging the controllers, which is ridiculous.