Hi, my name is Neil, and I'm a Windows 10 user like you.
It's true, my Xbox Bluetooth controller does not have a 'Power Management' tab under Bluetooth either, but looking under 'Human Interface Devices' (HID) it does (see pic below).
I have also located quite a few other devices before that were causing people problems where the Power Management tab does not show up where you think it should.
So with your Bluetooth headphones, looking in the HID is a good start. Have another good look and go through each device to make sure one of them is not your Headphones.
Sometimes when you click on the properties of a HID it will give you the Manufacturer of the Device on the General tab.
If you can't find your headphones there, look under "Audio inputs and outputs", "Other Devices", and "Sound, video and game controllers" too.
They should be listed somewhere.
Let me know how you get on.
Kindest regards,
Neil