Bluetooth
Use bluetoothctl (BlueZ) for devices that are already paired. Pairing a new device is the person's job: it often shows a code they must compare or type on the device, and the device must be put in pairing mode by hand. For that, open Settings on the Bluetooth page (slate-settings bluetooth) and tell them what to do; Settings answers the pairing request.
See what there is
bluetoothctl show # the adapter: Powered, Discoverable
bluetoothctl devices Paired # MAC and name of every paired device
bluetoothctl devices Connected
bluetoothctl info <MAC> # Connected, Trusted, battery level if it reports one
Tier: observe. No adapter in show: the computer has no Bluetooth or lacks its firmware; say so.
Connect / disconnect a paired device
bluetoothctl connect <MAC>
bluetoothctl disconnect <MAC>
Tier: reversible. Headphones become the sound output when they connect; wpctl status shows it (see the audio-volume skill).
Power
bluetoothctl power on # or off
Tier: reversible. If it fails with "Blocked", run rfkill unblock bluetooth first.
Forget a device
bluetoothctl remove <MAC>
Tier: confirm. Using it again means pairing it again, by the person.
Verify
bluetoothctl info <MAC> shows Connected: yes (or no after a disconnect).