You are overstating how much you need the terminal a bit. You can most certainly install and update software without the terminal. I get your point, but it's not 2006 anymore.
On which distro/s can I install all package types without opening terminal once?
You can install every native UI application and every Flatpak (or Snap) in every distro that ships with GNOME or KDE without opening terminal once. Not sure how the software center works for others but I'm sure they do the same.
Fedora, Ubuntu, Debian, Mint and many more. They all do it like this.
Need to install more than UI applications? Install dragora/Synaptic whatever GUI comes for your package manager. Not like you really need to do this because the average person only cares about the UI applications.
Have you used Linux lately? You can do this in any distro with a modern desktop manager. Discover in KDE Plasma, Gnome Software, and similar in other desktop environments are installed by default in the DE and have been for like a decade.
You are overstating how much you need the terminal a bit. You can most certainly install and update software without the terminal. I get your point, but it's not 2006 anymore.
On which distro/s can I install all package types without opening terminal once?
You can install every native UI application and every Flatpak (or Snap) in every distro that ships with GNOME or KDE without opening terminal once. Not sure how the software center works for others but I'm sure they do the same.
Fedora, Ubuntu, Debian, Mint and many more. They all do it like this.
Need to install more than UI applications? Install dragora/Synaptic whatever GUI comes for your package manager. Not like you really need to do this because the average person only cares about the UI applications.
Have you used Linux lately? You can do this in any distro with a modern desktop manager. Discover in KDE Plasma, Gnome Software, and similar in other desktop environments are installed by default in the DE and have been for like a decade.