While waiting I installed Recall box to try if it works. It's same there.
However... I found old Saitek Pad (PS2700) and it works like a charm. I decided to try xBox Controller via USB and it works like a charm.
Trying to connect via Bluetooth does not work at all. Will try to ssh and play with BT then, maybe console will tell me something.
Since I can't pair my headphones also, I think it might not be pad problem, but bluetooth.
About SteamController. There is problem with mapping of d-pad. It recognizes only swipe in one or 2 directions. Like Analog Left and Analog Up. So its more like Analogue for emulator than D-Pad.
But I think i can pass on stemController if XBox and Saitek works. I'm a fan of D-Pad. Touchpad as D-Pad is not good on SteamController.