The opposite is also true. You can’t officially use a Macbook in clamshell mode (eg, as a headless media server) even when connected to power. When you close the lid without a connected display, the official MacOS behaviour is to put the computer to sleep. You need a third-party tool to prevent it from sleeping.

Yet when my Macbook is asleep in my bag with no peripherals attached, my headphones will connect and wake the Mac.

The left hand does not know what the right hand is doing. It literally makes no sense.