What mixer and headphones are they?
I need to see if its even remotely possible.
Problems being the console needs to re-encode the audio in compressed format to fit through an optical cable. Seeing this model PlayStation only has Hdmi, it doesn't compress audio so the format would be 2.1 at best the mixer will receive.
Another problem is your headphones. If it's a type of headphone that uses software for 7.1, where's the software going to be installed to?
There are hdmi to toslink converters available but concerning video side of hdmi, there may be an adapter that passes video via another hdmi cable otherwise how do you get picture? Unless you go TV optical out and set the console to 2.1 as TVs dont compress HD audio either.