More than two channels driven means you'll need to be looking at AV receivers. The average amplifier will be 2 channels, sometimes with a subwoofer output, sometimes not.

Instead of buying some janky "Southsky" stuff, just buy an AVR. Used, if you want to keep the costs down. They contain all the digital decoding you need to use surround sources to do 3 channel, or 3.1 with a sub, or going to 5.1 to get the surround channels too.

By the way, you left out the most important part about that Amazon link, the actual item code. In fact you could skip everything but https://www.amazon.com and the item code. Not sure which "Southsky" you were linking to but maybe https://www.amazon.com/dp/B08KD9NVXY

If you already have a hdmi sound extractor you can add a "surround sound decoder". Assuming the extractor outputs surround sound i think this should work.

Sth like this one: https://www.amazon.com/SOUTHSKY-Digital-Decoder-Converter-Optical/dp/B08KD9NVXY

to do so, you will need this amazon link and you can do it via hdmi with this, you will also need to go in the PS4 settings and enable dolby or dts 5.1