To be fair, its largely because the Agile literature as a whole is vaguely written on the most important points.

Yes, everything is very unclear. It's also corrupted on most communication, either on purpose or by accident.

Corrupting Agile was once a very profitable activity.

Did I?

Where does the manifesto talk about a process of any sort? It’s a set of values. It doesn’t mention anything about iterations, breaking things down, etc

PDCA, in more humanities than engineering terms, is basically the final Agile Principle “At regular intervals, the team reflects on how to become more effective, then tunes and adjusts its behavior accordingly.”

https://agilemanifesto.org/principles.html

This is PDCA:

> Welcome changing requirements, even late in development. Agile processes harness change for the customer's competitive advantage.

And the sibling has the one that states PDCA for the development process too.