So I’m going to preface that I have never done this before but here is what I could find on the topic:
Hardware wise you could look into a Capture Card, has to be installed into the 3DS by opening it up. I see people offering this service on eBay for a fee.
I’m not sure these offer audio capture on top of visual, I imagine you will need to use an aux cable with some extra steps.
Actually accessing the capture is a different story, these cards don’t officially support macOS so you’ll have to use 3rd party software which may or may not be actively updated.
Software I saw mentioned:
cc3dsfs, CuteCapture, xx3dsfml, DualCapture.
No idea on their status though, so if you go this route make sure to look into it!
Software wise I found a tutorial on the Wiki Hacks Guide. TLDR you can stream visual only over wifi, audio being streamed via aux cable with some extra steps.
Thanks for the reply! I was hoping to avoid using a capture card and use a streaming service that used macOS but I struggled to find one. I’ll check out the guide you linked : D