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.
Your cheapest option because it’s FREE!
https://wiki.hacks.guide/wiki/3DS:Wireless_streaming#tabber-tabpanel-macOS_-_cuteNTR-OSX-1
Hopefully someone experienced chimes in!
🗣️🔥B A N G E R🔥