In the Edge browser there is a browser process running in the same appcontainer defined by its appx manifest, but there are also tab processes. These tab processes are running in restricted app containers that have fewer appx capabilities. The browser process has XAML loaded and coordinates between tabs and handles some (non-WinRT) brokering from the tab processes. The tab processes load edgehtml and that is where they render HTML, talk to the network and execute script.
The ApplicationContentUriRules (ACUR) section of the appx manifest lets an application define what URIs are considered app code. See a previous post for the list of ACUR effects.
Notably app code is able to access WinRT APIs. Because of this, DOM security restrictions are loosended to match what is possible with WinRT.
Privileged DOM APIs like geolocation, camera, mic etc require a user prompt in the browser before use. App code does not show the same browser prompt. There still may be an OS prompt – the same prompt that applies to any UWP app, but that’s usually per app not per origin.
App code also gets to use XMLHttpRequest or fetch to access cross origin content. Because UWP apps have separate state, cross origin here might not mean much to an attacker unless your app also has the user login to Facebook or some other interesting cross origin target.