Eh, yeah. I am on Debian Bookworm/kernel 5.14 with the Intel firmware-iwlwifi package - looks like there’s some regression with how the bluetooth firmware interacts with the machine. I was able to get the bluetooth working by replacing the firmware included in the sid/bookworm release (20210818-1, Intel release 28502) with one that was recently updated on the linux firmware git repo (Intel release 31586, checked into the repo on Sep 19th).
Copy the sfi file into /lib/firmware/intel, then power cycle your machine (shutdown, wait about 10 seconds, power it on again). The issue here is that while the bluetooth works just fine right after the power-on, any reboot will make it disappear. Resuming from sleep (not hibernation) is just fine, though.