That 404 page is using Local’s branded 404, which means that the Local Router is responding (that’s good!).
Looking at that terminal output, I’d be curious what’s in this file:
src/build/browser-sync.config.js
What it seems like is that browsersync is proxying localhost, but you probably want to be proxying the actual site-domain that the Local WordPress site is using.
See the BrowserSync docs for more info:
https://browsersync.io/docs/options#option-proxy
But maybe something like this needs to be added to the browser-sync.config.js file:
{
proxy: "mylocalsite.local"
}