What I gathered from trying to get a PS5 DualSense running on FreeBSD ( https://forums.freebsd.org/threads/playstation-5-dualsense-c... ) is the following:
BlueTooth 2.1 has full support. BlueTooth 4.0 has support only for Audio playback, anything else is unsupported. Thus if you get a BT2.1 USB dongle, Mice and keyboards should run fine as documented here: https://www.tspi.at/2020/02/18/fbsdbtmouse.html
PS3 controller works via BlueTooth problem free via btsixad, DualSense and PS4 controller lacks drivers.
Using just jails on my servers, no idea about docker.