I've had a laptop that I've never been able to get WoL (Wireless or otherwise) to work, no matter what I tried. Recently realized that the Bluetooth keyboard I used was able to wake it with a key press though.
I must be too old school because my first thought when i read this was “with an old solenoid lying around and a few lines of code, an AtTiny could strike a key on the bluetooth keyboard, waking the laptop!
I'm mildly surprised OP's laptop keeps the bluetooth radio powered up while asleep, but I would be a lot more surprised to find one that doesn't work with USB HID.
I actually tried something like this, the laptop BIOS didn't have any settings to tweak for A/C power changes. However, it does wake from sleep after plugging in. The issue is, it immediately goes back to sleep (within seconds). Tried quite a few things to try to stop that behavior (e.g. running Power Toys Awake) but had no luck.