I stream a lot games in my PS4 and i can see my Alert Box or any other integration on my stream. Please make this!
By the way, if you use a USB 2.0 plugin capture card it is easy to use this to have stream-labs obs as your broadcaster. the only thing is you won't have the stuff on the big screen you use your ps4 on. that's my suggestion until its added or decided they are or won't do this suggestion.
of course, you can use any other compatible caster program too.
You won't be notified about changes to this idea.