To (re)pair the Steam Controller (2015) you have to open Steam app, go to Settings>Controller>Add new controller, then to pair it with dongle, hold X then press Steam button. You might also need to switch to Dongle mode first by holding A then pressing Steam button.
To pair it via bluetooth hold B press the Steam button.
Pairing on Raspberry Pi (tried 4b+) didn't work even though steam-devices package was installed.