I got the exact same issue of the missing icon on Pop!_OS 22.04 LTS when installing version 2.6.1

When installing cider-linux-x64.flatpak with the command:

flatpak --user install cider-linux-x64.flatpak

I got this warning which is likely related to the issue:

Warning: Not exporting file sh.cider.genten.png of unsupported type.

I managed to find a workaround for getting the icon working, however your millage may vary.

Missing Icon Fix

In the terminal:

mkdir -p ~/.local/share/flatpak/app/sh.cider.genten/current/active/export/share/icons/hicolor/256x256/apps

cd ~/.local/share/flatpak/app/sh.cider.genten/current/active/export/share/icons/hicolor/256x256/apps

cp ~/.local/share/flatpak/app/sh.cider.genten/current/active/files/lib/sh.cider.genten/resources/public/icon.png ./sh.cider.genten.png

mkdir -p ~/.local/share/flatpak/exports/share/icons/hicolor/256x256/apps

cd ~/.local/share/flatpak/exports/share/icons/hicolor/256x256/apps

ln -s ../../../../../../app/sh.cider.genten/current/active/export/share/icons/hicolor/256x256/apps/sh.cider.genten.png ./sh.cider.genten.png

Then:

update-desktop-database

If the icon is still not showing up try rebooting.