For the icon to work correctly, it needs to be copied from there:
/var/lib/flatpak/app/sh.cider.genten/x86_64/stable/active/files/share/pixmaps/sh.cider.genten.png
to here:
/var/lib/flatpak/app/sh.cider.genten/x86_64/stable/active/export/share/pixmaps/sh.cider.genten.png
Then, for the kde integration with the media player widget, use flatseal to modify the permissions under the Session Bus:
Talks:
org.mpris.MediaPlayer2.Player
Owns:
org.mpris.MediaPlayer2.cider
Then the media player widget will appears whenever cider isn't stopped. The multimedia keys will work too.