Looks like the icon is in the wrong place in the flatpak, so isn't being exported - it should be in /app/share/icons/hicolor/$size/apps, but is in /app/share/pixmaps (ref doc that lists the required location: https://docs.flatpak.org/en/latest/conventions.html#expected-standards).
There's also a couple of session bus issues - it requires the following to show the status (tray) icon and have working desktop integrated media controls.
[Session Bus Policy] org.kde.StatusNotifierWatcher=talk org.mpris.MediaPlayer2.cider=own
Unlike the icon, you can work around this before it's fixed by adding local overrides with Flatseal or the following commands:
flatpak override --user --talk-name org.kde.StatusNotifierWatcher sh.cider.genten flatpak override --user --own-name org.mpris.MediaPlayer2.cider sh.cider.genten