Small progress: I added a symbolic link from /var/lib/bluetooth to /tmp/bluetooth (via rootfs_overlay) but I still have the same error.
(bt-agent:363): GLib-CRITICAL **: 13:30:51.254: PCRE library is compiled without UTF8
(bt-agent:363): GLib-CRITICAL **: 13:30:51.255: PCRE library is compiled without UTF8 properties support
bt-agent: bluez service is not found
Did you forget to run bluetoothd?
Now I don’t understand what the problem is since I don’t have any error anymore (neither from dmesg nor from bluetoothd).
