I can now confirm that my half-broken range extender is considered the same network, and the streaming works.
I still bought a new mesh extender as a back-up, but this is perfect for what I need.
I've hacked 3DSes before, but they were the "old" models, so I'm not familiar with the capabilities of this.
Due to how my house is set up, my PC is on a 20m LAN cable to the router, with a range extender for my phone and 3DS. I got a Pokéball...
I get what they were trying to say but what the ad actually says is "we tried to cram a ton of features into the iPad but all of them got irreparably mangled
in the process."