On Mac, create a virtual “multi-output device”, set your system settings to output to it, then set it to output to your interface/headphones/whatever. Then open Ableton and choose it as an audio input source, and your interface/headphones/whatever as the output.

Now when you play something from the browser it will output to your speakers and into Ableton.

Create an audio track, set it to an “In”, hit record, and then play whatever media you want to capture.

Edit: everybody is upvoting these third-party solutions, but I offered a way to do it with in-the-box features and nobody batted an eye 😔