No controller in Steam

Hi all, I can run Steam, but my PS4 controller is not recognized by it - Steam cannot be controlled, it will not assign it my profile (the LED would change color from default blue)

  • Games that do not register it (overlay cannot be activated either): Everything, Tomb Raider
  • I found one Steam game which does register the controller: FEZ

I use the flathub version, same as previously on opensuse Tumbleweed where the controller would be recognized as long as it was plugged in before launching Steam. I retained the ~/.var/app/com.valvesoftware.Steam directory.

$ flatpak info -M com.valvesoftware.Steam 
[Context]
...
devices=all;

lsusb lists the controller.
I found this when launched from terminal – controlled cannot be open, but it does see my mouse (it has few controller-like buttons):

Local Device Found
  type: 054c 05c4
  path: 0003:0009:00
  serial_number:  - 0
  Manufacturer: 
  Product:      
  Release:      100
  Interface:    0

Unable to open local device: 0003:0009:00
Local Device Found
  type: 1e7d 2e4b
  path: sdl://0
  serial_number:  - 0
  Manufacturer: 
  Product:      ROCCAT ROCCAT Tyon White
  Release:      111
  Interface:    -1

Any ideas please?