How do I stop Bluetooth from waking a closed, sleeping MacBook Pro?

How do I stop my Bose Bluetooth headphones and other Bluetooth devices from connecting to my MacBook Pro while it's closed and asleep?

"Powernap" is disabled for both battery and plugged in.

I know this is happening because the Bose Bluetooth headphones have audio prompts that say "Connected to MacBook Pro".

This is annoying because among other reasons it seems to wake the computer up (at least partially) and cause it to lose a lot of battery power while it should be asleep. Nothing is running that should cause this, usually just a web browser.

This was a problem with both Mojave and the new Catalina OS.