Signaling is a very app-specific question, as you can use a wide range of options. If you take a look at the "apprtc" example, it's a demo which uses appr.tc's signaling.

You can indeed use aiortc facing a browser, itself or any valid WebRTC endpoint.

Sure, you can use aiortc for a desktop application. However for this specific usecase embedding a browser which supports WebRTC (say QtWebEngine) might be a good option too.

Naive question: what's cool about doing webrtc outside a browser?

If you are trying to build e.g. Twitch or Discord, you want to have a server backend to handle processing, hide user IPs from each other for privacy etc. (the term you are looking for is single forwarding unit). If you just want to get something up quickly, I recommend OpenVidu.

If you're hiding everything behind a server, couldn't you just use WebSockets? I thought the whole appeal of WebRTC is the whole peer to peer setup.

WebRTC provides audio and video streaming, as well as unreliable/unordered data transport through data channels, which is really great for games.

You can't use UDP with web sockets.

Maybe you want to do something audio/video based, don't want to reinvent the wheel and more importantly you absolutely don't want a web browser running on the system running your application (for example because you're running on an embedded system)