SC Controller [GitHub], the rather great driver and user interface for working with the Steam Controller (and now many others) outside of Steam recently added Bluetooth support.
Version 0.4.3 was released only three days ago and it comes with a pretty impressive list of changes. The Steam Controller, the Sony Dualshock 4 (PS4 gamepad) and all other Bluetooth pads recognised by evdev are now supported.
It also fixes unexpected behaviour when ring bindings are combined with pad clicking.
It now comes with a rather nice AppImage, which should work across all distributions. No compiling, no hunting for packages. Just download, make it executable and run.
Such an incredibly useful project, especially since I love my Steam Controller and this makes using it in GOG and itch.io games an absolute breeze.