That song is directly inspired by the Pepsi nonsense; the lyrics and backing video [1] have some direct quotes. Definitely the first thing that comes to mind each time a multi-billion company decides to change their logo and nobody likes it.

[1]: https://www.youtube.com/watch?v=fu3ETgAvQrw

It recalls to mind Don Quixote. Is it madness or genius? In the case of great art; who can rightly say.

It is clear they worked hard for their salary.

"Redesign Your Logo" was actually directly inspired by this exact brand redesign document, so your instinct is well-founded! Here's a transcript of the official Spirit Phone commentary track where Neil mentions it:

https://lemondemon.fandom.com/wiki/Spirit_Phone:_Commentary#...

(i think it was also released as a joke, then everyone took it seriously)