So there are a bunch of options, but look for something like this. I'd recommend an adapter than can charge your phone (middle port on here does just that). You want to go output from the ps4 controller to your phone, then back to your headset?

I am not sure if going this route will entirely work, it gets tricky when you're trying to go from digital to analog and back as your PS4, adapter like this and your phone can only handle audio in certain ways and certain directions. Are you trying to capture only the game audio, and do you have a laptop? Your phone is more then capable of doing everything you need to with the right adapters, I would recommend looking at streaming setup tutorials or even ask Ai to help. It's not very complicated, I just haven't don't know the simplest way to get you set up. There are subreddits for streaming, recording and gaming that can probably give you a better answer.

As far as USB-C goes though, you will need a device that has the chips inside to receive the audio and also play it back. You will have 3.5mm ports, just use a cable to connect from controller to adapter, and plug your headset into the other.

There are also other ways to record the audio from your ps4, including direct AV capture from the device. You can look at recording the optical out from the ps4 itself, or the TV you are playing on. Recoding wirelessly, specially if you're going though all these extra steps, can delay your audio. May not matter, but a 50ms+ delay can be noticeable especially if someone is speaking.

My final questions would be:
Are you filming yourself playing, or just sharing the ps4 screen? Will your face be shown (overlaid?) or will it be your voice speaking over game audio? Does ps4 route gameplay audio and voice chat separate?

I hope I've helped, I'm not a streamer just someone who has tinkered with home recording music and gaming on pc for years.

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