Something like 99% of the use cases I've seen for OpenBSD are servers that have no keyboard, mouse, video, audio or other plugged into them. It's completely unsurprising that bluetooth and gamepad support isn't a priority.
The Bluetooth stack on linux is literal code trhown away from qalcomm (or was it broadcom?) with dbus on top. But since they dumped it as GPL it won't reach BSDs.
The rumor is that OpenBSD devs run it on Thinkpads while most FreeBSD devs are using MacOS as their main OS.
As a gamer & dev running Linux, I pass-through bluetooth hardware into a gaming VM for controllers and don't even have bluetooth stack on host.