For my Thinkpad X1 Carbon 3460 I finally picked apart the bluetooth driver supplied by Lenovo.
Just to get rid of these pesky bootmessages:
Bluetooth: hci0: BCM20702A1 (001.002.014) build 0000 bluetooth hci0: firmware: failed to load brcm/BCM20702A1-0a5c-21e6.hcd (-2) bluetooth hci0: Direct firmware load for brcm/BCM20702A1-0a5c-21e6.hcd failed with error -2 Bluetooth: hci0: BCM: Patch brcm/BCM20702A1-0a5c-21e6.hcd not found
Here is my own short summary, based on these explanations:
To prepare, download the firmware supplied by Lenovo, and, as root, create the target directory, and install the innoextract tool:
mkdir /lib/firmware/brcm apt install innoextract
As normal user, unpack the driver, find the right hex file, and convert it.
innoextract g4wh01ww.exe cd app/Win32 hex2hcd BCM20702A1_001.002.014.1483.1669.hex
Lastly, as root, copy the file while giving it the right name:
cp app/Win32/BCM20702A1_001.002.014.1483.1669.hcd /lib/firmware/brcm/BCM20702A1-0a5c-21e6.hcd