I'm pretty sure the answer is "Nope, nothing like it" but as a new PS4 user and long-time PC user its possible there's a solution I've overlooked. Is there a way on PS4's version of Overwatch to accomplish a voice chat equivalent to Discord (your friends) and in-game team chat layered? On PC I'd set up Discord and get on with friends while playing, but still allow Team Chat from Overwatch to play audio out, and bind a key as push-to-talk in Overwatch (and in Discord, push-to-mute so I don't echo to my friends, but honestly this part is optional).

The end result was I could hear my friends all the time as well as team-chat, and could use push-to-talk to switch which audio-in my microphone went to.