These are the buttons I found that are expressed on a PS4 controller.
You won't see the correct buttons inputs appearing up in-game.
Instead it shows a generic button #1-12, as you could see in the screenshots.

Movement - L-Stick (Left Analog Stick)
Camera - R-Stick (Right Analog Stick)
Jump/Dodge - Square
Kick - X
Punch - Circle
**Confirm "aka Button 1" - Square
**Select "aka Button 3" - Circle
Cancel "aka Button 2" - X
Interaction (gear icon) - Triangle
Aim - L1
Spammer* - R1 (while aiming)
Junk Bolt* - R2 (while aiming)
Sensen Menu - Option Button
Game Pause Menu - Share Button
S-Pressen Wheel - L2
Aug-Eye - L3 (Left Analog Stick Button)
Center Camera - R3 (Right Analog Stick Button)

*if I recall correctly, you need to unlock the ability to use the spammer and junk bolt.
**For some reason the in-game tutorial messages and S-Pressen Wheel uses "Button 1" to continue, oppose to "Button 3" which is used for everything else in the game.

Climb/Jump - Square
Drop/Release - Triangle

Rewind - Counter-clockwise Circular Motion on 'L-Stick' / 'Mouse'
(hold 'R1' / 'LMB', to rewind faster)
Pause - Leave your 'L-Stick' pointing in any direction?...
(hold 'L3'? / 'RMB', to pause/stop playback)
Play/Resume - 'L-Stick' in neutral position
Interaction (gear icon) - 'Triangle' / 'E'
Navigate Gltches - 'R-Stick'

To rebind your keys, you go to the Game Menu > Bindings.
Select "Select input device" by hitting "Confirm" button (circle),
To toggle between "Keyboard and Mouse" to "Wireless Controller", hit left or right on D-pad or L-stick.