@AlexFalkor I don’t know if you’ve solved your problem yet, but my best suggestion would be to buy a cheap USB Microphone for your PS4 and just plug it in and set it on your desk. I ran into several problems when setting up the elgato to stream PS4.
Audio Lag: When running the elgato through the PC there was about a 2 second lag I had to solve. I fixed it by plugging in headphones to the TV itself. You cannot use a headset on the PS4 while using the Elgato because your sound needs to go through the HDMI cable. If you route the sound through the USB on your PS4 it will cut the sound to the stream.
Real Time sound for OBS: I found that streaming a game with a 2 second sound lag is pointless and nearly impossible. Plugging in headphones to the TV is nice, but then you can’t hear your sounds on your computer when you get a follower, donation, etc. I solved that by hooking my PS4 and my PC together using a 5 channel mixer bought for about $40 and a couple cords.(Caveat would include needing your tv, computer, and ps4 all right next to each other)
Webcam/Sound lag in OBS: This was the easiest and obviously cheapest to solve, but you just need to offset your webcam and sound on OBS to match the lag of the elgato.
It’s a pain in the butt. but 100% worth the investment IMO. I can play games and listen to music/talk to people on my pc while listening to my ps4 or any other HDMI device at the same time
EDIT: The last thing I ran into was talking in party on my ps4: That is fixed by buying a cheap table top USB mic for the ps4, and set it on the desk. The PS4 should detect most microphones on the market and the sound from the party will go through the mixer, and your voice will go through the mic on the desk. All sound will go through OBS to your stream, and you just have to use 2 mics. This is nowhere explained on YouTube, Elgatos website or anything. Which is why I’m thinking about making a tutorial for it.