But GUIs never took off as a UI for a general purpose computer, they became the UI for application on a general purpose computer. For them to be the former requires them to be programmable. Smalltalk is the best/most-famous example of a Graphical UI for a general purpose computer I can think of...

The main point is that for a general purpose computer the UI needs to integrate programming. Programming is how you use a computer. The shell (text) is currently the primary UI that inherently allows programming.

Is a modern phone a general purpose computer?

What kind-of UI does a modern phone present?

A modern phone is not a general purpose computer. They are proprietary, locked down devices. Appliances.

"The PinePhone is a smartphone that empowers users with control over the device. It is capable of running mainline Linux, features hardware privacy switches, and is designed for open-source enthusiasts."

Perhaps I simply failed to see your definition of "a general purpose computer".

Please say what rules must be passed to meet your definition.

CLI is also specific to apps in practice, and I don't see any obvious difference between scripted CLI and scripted (with the likes of Active Scripting or AppleScript, or for that matter Tcl etc) GUI apps.

The difference is that you don't use Active Scripting, AppleScript, TCL, etc. as your primary UI. The shell is a script-able UI.