documentPictureInPicture.requestWindow() hands back a second
same-origin Window, with its own
navigator.mediaDevices. This page calls
getDisplayMedia() from three places: here, from the PiP
window's own realm, and from this window's realm but triggered by a click
inside the PiP window. Compare which window the share picker is attributed
to, and whether a click in the PiP window counts as transient activation
for its opener.