As the "graphical update tool" is just a basic wrapper for the normal updater, I would be very surprised if any distro coming with a desktop environment by default has none...
So the answer would be "every single one but Archlinux (nothing by default but the base system) and server installations"
(PS: My "graphical" updater on Archlinux is a handful of very small scripts that a) runs checkupdates and flatpak remote-ls --updates from time to time writing the result into a temp file, b) displays an indicator if that file isn't empty, c) prints out the file as a notification on clicking that indicator and d) runs pacman -Syu && paru -Syu -a && flatpak update && pacdiff in a terminal window when I right click the notification.)
(PPS: Small correction... Manjaro doesn't have graphical updater but a buggy abomination prone to fucking the AUR instead.)