Hi, I dont have experience with phaser. I work with godot and a bit with unity. It looks like there are some tutorial on YouTube but aside that I can only tell you the overall logic behind parallax.
Each layer has a specific speed applied to it under certain condition. It can be automatic scrolling (like in my shooting game ... the plane does not really move if you dont touch control, the layers of parallax do)
It can also be when you press a key. Right or left for example will apply a scrolling speed as long as you press the key. This will give the feeling your caracter is moving when in fact, the background is.
You can have a combination of both and other techniques.
The infinite feeling is provided by a mirror effect. The layer reappears "outside of screen" so the player never see the cut.
Again I checked quickly and you have some tutorial on YouTube. Let me know if it worked.