I wanted to know if I can use the Turtle Beach Stealth 700 'headset via cable on the PS4 Pro, e.g. Connect to a controller…
Well, you can use it wirelessly on the PS4.
With cable not '?
Have a look here, there are all possibilities listed:
https://support.turtlebeach.com/hc/de/articles/115000228973-Stealth-700-For-PS4-PS4-Pro-Kurzanleitung