Can't share other windows with Chromium Flatpak

When using the Chromium flatpak, I can’t seem to share other GNOME windows using common meeting platforms like BlueJeans and Google Meet. I seem to recall being able to do this - either in a prior version of Chromium, or when running Google Chrome inside of a toolbox.

Chromium version: Version 95.0.4638.54 (Official Build) (64-bit)
OS: Fedora 34 Silverblue (v34.20211103.0)

Is this a known issue?

Note that this is NOT direct screen sharing - this is a known issue with Wayland that has existed forever now.