I’m assuming you’ve already verified that other bluetooth devices work as expected.
A different distro (e.g. Debian Stable) might help narrow down the problem, as their kernels tend to be built with different options and their packages sometimes have different default configurations. Be sure to look for helpful messages in dmesg and syslog/journalctl.
After that, the next thing I would try is a USB bluetooth dongle. Some bluetooth modules don’t work well with Sony’s controllers, and it’s possible that the one on your motherboard is among them.