@Artex Just installed Yandex on Linux, and PiP has this window frame which obviously shouldn't be there.
52443d33-a08e-4e6e-b7f9-b64bef48a902-image.png
Also noticed a bug that subtitles get stuck after I minimize the main browser window. So again, far from perfect, Vivaldi's PiP is much better on Linux.
The Firefox implementation that I mentioned in my previous post, is the same for Windows and Linux. It even allows to have multiple PiP windows at the same time, so yeah, I guess they nailed it, unlike Chromium.