How can I store / download the recording from the Screen Capture web API?

I'm using the Screen Capture API and am trying to save the final capture to a video file (WebM, MP4, etc.). I have these two JavaScript functions:

async function startCapture() {
    try {
      videoElem.srcObject = await navigator.mediaDevices.getDisplayMedia(displayMediaOptions);
    } catch(err) {
      console.error("Error: " + err);
    }
}

function stopCapture() {
    let tracks = videoElem.srcObject.getTracks();
    tracks.forEach(track => track.stop());
    videoElem.srcObject = null;
}

The video is displaying live fine when the capture is started, but I'm not sure how to actually store its contents. videoElem is a Promise that resolves to a MediaStream. tracks is an array of MediaStreamTrack objects. This is my first time doing any kind of web development, so I'm a bit lost!

Recording a media element on the MDN docs helped me a ton. Basically, instead of using getUserMedia(), we use getDisplayMedia().