I cannot select the Adwaita icon theme from Desktop>Appearance>Experimental Settings>Icons and toolkit theming.
I just checked it with the pop_os ISO there it is possible.
I am running Fedora 40 Workstation with all the latest updates applied. When using gnome-tweaks the Adwaita Icon theme also shows up.
AFAIK, the Adwaita icon theme does not follow the freedesktop spec
Plus, it contains Hidden=true on my pc
Hidden=true