LibreOffice uses its own widget toolkit. It works similarly to wxWidgets, basically just maps to whatever toolkit is native on the current platform. It uses Win32 on Windows, Cocoa on macOS, Qt on KDE, GTK on GNOME and a few others.
That said, their current approach to dark themes is pretty bad. It can very easily conflict with the dark theme from the host toolkit and cause issues if misconfigured, which has caused a lot of people to think it just doesn’t work. It does work, but it can be confusing as hell to configure correctly.
For instance, LibreOffice has a setting you can use to change the application colors. It barely works and you should never touch it. Just let it get the colors from your toolkit.
There’s also the fact that LibreOffice doesn’t use FDO icons and has its own icon setting which doesn’t automatically follow dark/light theme. If you’re using a dark theme, you have to manually switch the icon set to one that isn’t impossible to see on a dark background.
Oh and if you want your documents to use a dark palette that’s also a separate setting. Like I said, confusing.