Hi and welcome (back, I think
)
Biggest problem you have is the "slim" part of your PS4. There's no optical on that unit, so you're forced to use HDMI. HDMI into TV can cause lag. And the choice of TV and settings willl make all the difference.
If you have HDMI going into an audio amp, change amp settings to STRAIGHT, or PURE or whatever your amp will do to output simplest unproccessed audio. You do not want full fat Dolby surround, pro-logic, simulated atmos or any of that. Any kind of processing will introduce lag.
If you have HDMI going into TV and using those speakers, then make sure you use GAME mode on TV, and just go through all the settings and turn every kind of picture or sound processing off. If no game mode, select a preset to use and turn off every processing available.
If you have HDMI going into TV then sound out to amp, you can do both the above, but I doubt that will fix anything as you've introduced another link in the chain.
I haven't had the need to try the splitter/extractor route as I have original PS4 with optical out, but I still set amp to STRAIGHT. That makes a difference.
I have read that USB extractor to optical (Spidif) is supposed to not introduce lag, so that might be your best bet. That's if you can use the optical spdif signal
I can't say how good they are or what cabling you need into amp/headphones, but here are a few that might help.
Amazon product ASIN B01N905VOY 3.5mm output for headphones/soundbar/amp. If it's just headphones, have you tried the headphone jack on the PS4 controller?
Amazon product ASIN B07K24FD4K with red/white/L/R RCA and 3.5mm for amp/soundbar.
Amazon product ASIN B00XJITK7E This one uses HDMI, so you can take HDMI from PS4, pull sound out using RCA (red/white/L/R) or Spdif (but no 3.5mm) to amp or soundbar, then HDMI onto TV for video.
Amazon product ASIN B08P7CHQYF looks to be the same as above, but replaces the RCA with a 3.5mm joack for headphones or amp/soundbar input.
Can't find anything in the PS4 audio setup, other than on mine I have option for HDMI/Optical (which I use) and LPCM (Which I use), Dolby bitsream.
Pretty much need to know what you are planning on using for your sound output. TV speakers (What model TV you got?), soundbar, external powered speakers, Audio amp, or just simply headphones.
Let us know how you connect at the moment. What TV you have, whether you use an amp or soundbar, and I'll do my best to point you in the right direction.