There is a bit of categorical mixing going on and the author fails to identify actual hierarchies within the programming styles. But he does see, correctly, that it all has to do with state management. I'll point out what he got mixed up:

First OO programming is a specific style of imperative programming. OO is simply imperative programming with state and functions scoped into instances. If you are doing OO, you are also still doing imperative programming.

You can't really compare OO to functional because it would be like comparing a very specific concept to a very general concept. Like comparing cars and planes, but instead you're comparing a 2020 tesla with all planes in general. No... either compare specific cars with specific planes or planes in general with cars in general.

Declarative programming, on the other hand, can be stateless or stateful so it doesn't really apply here. Declarative programming is sort of left field to all these programming styles because technically chatGPT is declarative. Declarative programming is more about linguistics, AI and natural language processing. It's completely orthogonal to state management.

Functional programming and Imperative Programming are the two correct categories to compare here. They are siblings in the hierarchy and they are distinct and in essence simply two different ways of handling state.

Case in point: If you change one thing in your imperative programs. One thing... then your imperative program immediately becomes functional.

This thing is immutable state. Imperative programming with immutable state IS functional programming. Change the way you manage state, then you essentially change the name of your programming style.

The two paradigms are in essence two different styles of state management. All the other stuff with OO and Declarative is sort of fluff and distracts from the true essence of the isomorphism the author noticed here.