StudioLive Series III sample rate is not supported above 48KHz.
The console supported operating sample rate is 48KHz. See Tech Specs of console here: https://www.presonus.com/products/StudioLive-32/tech-specs
Scroll down right column to where it says, Sampling Rate.
If you open a 96KHz session in Studio One and your audio interface max sample rate is 48KHz, Studio One can convert the entire session to 48KHz for you.
If you recorded into your DAW at 96KHz in one interface and then connected the StudioLive III at another time to be your output, the session could be converted to 48KHz to be able to play out.
To support higher sampler rate conversion in / out you'll select a hardware solution that has the sample rate range you require. You can use the Studio Series interfaces or Quantum if you require higher sample rates above 48KHz.