I have been on the hunt for what exact shortcut the controller hides from us. But there is a steam menu (controllers, advance, show more, at the button) that shows them!

Quickly want to change your volume? Try steam key + left joystick!

Sadly you can not change anything here, altought the menu shows you you can, nothing will be saved after you leave a menu. (I'm not a fan to put the left mouse button on the right button)

A few of them I manually found before written out, also for the people without images:

hold A + R1 + Steam
To use Puck wireless mode right

hold A + L1 + Steam
Start Puck wireless mode left

hold B + R1 + Steam Start Bluetooth mode

When on (solid white)

Steam+Y Turn off quickly

Hol steam (10s) Turn off

Steam + left joystick up/down Change volume level

R4 + R5 + L4 + L5 + Steam Backpack mode (ignore buttons until this combo is used again or USB)

Steam + Right trackpad/joystick Mouse movement

Steam + X On screen keyboard

Steam + R1 Take screenshot

Steam + Menu ALT+TAB

Steam + D-pad right Enter key