I have it hooked up to the trigger out in my AVR (which I only use because it has HDMI ARC). So it’s off anytime my TV and AVR are off.
As for my headphone DAC/AMP, both the one in my office and the one on my sim rig are off unless I’m using their respective computers.
Haven’t tried too many pairs of headphones but the Focal Clear MG fit me like they were made for my head.