I’ve created a Kubuntu 21.10 virtual machine and I can reproduce your issue.
My guess is that KDE is expecting the icon in a different place. Compare ConverterNOW with TextEditor (which displays correctly in KDE):
$ find /var/lib/flatpak/exports/share/icons -name io.github.ferraridamiano.ConverterNOW*
/var/lib/flatpak/exports/share/icons/hicolor/256x256/apps/io.github.ferraridamiano.ConverterNOW.png
$ find /var/lib/flatpak/exports/share/icons -name org.gnome.TextEditor*
/var/lib/flatpak/exports/share/icons/hicolor/scalable/apps/org.gnome.TextEditor.svg
/var/lib/flatpak/exports/share/icons/hicolor/symbolic/apps/org.gnome.TextEditor-symbolic.svg
So I would use the SVG file (I hope you have it) and install it to .../hicolor/scalable/apps/
.