@notorious Yes. Even after restarting Vivaldi, the size and position of the PiP window is remembered. The current PiP window is closed after restarting Vivaldi, but I do not think that matters.
I noticed the Picture-in-Picture button for video is not available on Facebook, either. (At least not on the new Beta interface on Facebook Live videos being watched after the fact, i.e. no longer live). Presumably it's the same problem, where Facebook is not actually using an HTML5 player.
It's needed to add an official extension for twitch to work with PIP,
https://chrome.google.com/webstore/detail/picture-in-picture-extens/hkgfoiooedgoejojocmhlaklaeopbecg?hl=en