I can confirm that this issue is still present in the latest debian-live-12.6.0-amd64-kde.iso
I've also checked other official Live ISOs. GNOME, LXDE, LXQT, MATE, XFCE have install-debian.desktop files at $HOME/Desktop. For some reason, it's missing there on the KDE Live edition. "Install Debian" launcher still can be found in the "System" category of the "Application Launcher" I believe that this location is a lot less discoverable than either icon on the Desktop (LXDE, LXQT, MATE, XFCE) or pinned launcher on the Dash/panel (GNOME). This is probably a Debian 12 regression, as this launcher is present at $HOME/Desktop (and visible for the user) in debian-live-11.10.0-amd64-kde.iso
