So a “cell phone” is a “general purpose computing device” but a console isn’t?

They're both Turing machines, if that's what you're getting at.

In practice, no, a console is not a general purpose computing machine.

On iOS, by design, you can install almost any kind of application even without jailbreaking it. Which people do, you can have Excel and Maps and IDEs and whatever.

Consoles, by design, do not allow that. It's almost strictly meant for games and media.

And again. I don't care. Both types of walled gardens should be abolished.

There is nothing about consoles that make them incapable of installing any type of software. They support keyboards and mice.