In other words, how to connect MacBook Pro (Retina, 15-inch, Mid 2015) to Apple Studio display? What cables/adapters to use?
The latest Apple Studio Display (2022) uses a Thunderbolt 3 connection for video. You will need this adapter to connect to the monitor and this cable to connect with the Thunderbolt 2 port on your MBP.
Don't skimp on these two accessories. If you can find similar Belkin or Anker items, those are acceptable substitutes. Years of testing adapters and cables of all sorts for my job has lead to these two manufacturers (other than Apple-branded items) as having the best build quality and proper specs. (Apple-recommended items also make the grade, or Apple wouldn't make them available in their store.)
Disclaimer: I have no financial interest or ties with Belkin, Anker or Apple.
With Apple's TB3 adapter and TB2 cable, Studio display could identify and re-arrange/change resolution by my MacBook Air early 2014(Catalina) and it works with keyboard connected to it. But the display does NOT show anything and the brightness seem not configurable. Not sure if it works in future, but at least the display doesn't work for now.