I honestly don't think the average Google Chrome user knows what a 'local' device is, and we should go something more ELI5 "This website wants to spy on every other device connected to your network" or something

Since I can see legitimate use case (complex web apps, one sharing data with another) - I would not use the word spying.

But still make it clear what can happen.

"Attention! This website wants to get access to other web apps running on this device, do you want to allow this?"

And then a link explaining some more. But better words are surely possible.

I need to turn on location access for all software on my system globally to read the battery status of a device over Bluetooth. These "could be used for" warnings are nice and all, but usually goes beyond what makes sense. Proposing that we need to press "be spied upon" just to view photos stored on your NAS is way out there

I'm sorry if people don't know what "access local devices" means but actively lying to them about the mechanisms is not going to inform anyone

Most of the time this prompt comes up it's actually for a genuine purpose, like spotify trying to find devices on the local network that can play audio, VLC looking for chromecasts, I saw my DJ app ask for local network and discovered it can discover my decks on the network and stream my library over the local network to it.

The problem is this prompt is new so the software doesn't show the user why it's just triggered the prompt and the user has no info to work with.