I guess OBS? Works on Windows if you use the webbrowser and disable Hardware Acceleration. Be advised though, the resolution and bitrate on browsers alone could be limited and also on linux clients.

I think the best way is still to rely on already ripped content. Though if you want to start creating webrips yourself, afaik people use their cookies and use the streams, that the browsers/applications get pushed and turn them into other video formats. But not at all a pro on this topic. Someone else here is surely better informed than me on this topic.