The built-in media player in Chrome OS now supports Picture-in-Picture. I have this working in the Canary version of Chrome OS. Here is how to use Picture in Picture.
Open the Files app and play any video.
Now, click the three dots menu on the bottom right corner and choose Picture in Picture.
The video will now start playing in Picture in Picture mode. You can drag or re-size this Picture in Picture window.
Try this out and let me know what you think!
Note: This may not be available in Stable version yet.