GTK3, GTK4, and libadwaita applications do look native in COSMIC. In COSMIC Settings, navigate to Desktop > Appearance > Icons and toolkit theming. Or search "toolkit" and it will be a top result. In the context drawer that opens on the right, toggle "Apply current theme to GNOME apps". This will then allow the cosmic-settings-daemon to automatically generate CSS variables for GTK4 and libadwaita apps. If adw-gtk3 is installed, it will also apply those variables to GTK3 applications.
Qt4 and Qt5 applications are unsupported, but IgKh/CuteCosmic has a Qt6 Platform Theme that integrates with the cosmic theme system and applies that theming to Qt6 applications. Though it won't work in 24.04 because most of the KDE/Qt apps in this release are based on Qt5, and the version of Qt6 is too old.
Qt4 and Qt5 applications are unsupported, but IgKh/CuteCosmic has a Qt6 Platform Theme that integrates with the cosmic theme system and applies that theming to Qt6 applications. Though it won't work in 24.04 because most of the KDE/Qt apps in this release are based on Qt5, and the version of Qt6 is too old.