Bluetooth seems to be a pain point for libre solutions. Has Purism published any details of the Bluetooth hardware in the Librem machines (are they all the same?). What is the exact model of the chip(s) used?
More exactly the Bluetooth is an AR3012 conected to USB but it is built into the WiFi module along the AR9462.
The AR3012 is a BT4.0 incl. low energy (aka “smart”) capable chip, based on a 32-bit CPU core by Tensilica which is again a MIPS derivate (AFAIK).
There is only little information available on the AR3012 and what this “firmware” is actually doing. There is a brief product flyer available e.g. here:
The Tensilica CPU cores are supported by the Gnu tools (GCC, binutils, gdb), maybe a round of disassembling might come up with something useful? Since the total binary code is ~50kb I doubt that this is the complete baseband. Using “strings” on the binaries already gives some insights.