As ruben2020 wrote in a comment this sounds like shunyata.
I am not the best person to explain that.
Wikipedia's Śūnyatā is long and maybe the doctrine has differed some according to different schools.
Its Prajñāpāramitā sūtras section includes wording that's similar to what you quoted:
The Prajñāpāramitā (Perfection of Wisdom) Sutras taught that all entities, including dharmas, are empty of self, essential core, or intrinsic nature (svabhava), being only conceptual existents or constructs. ... The Prajñāpāramitā sutras also use various metaphors to explain the nature of things as emptiness, stating that things are like "illusions" (māyā) and "dreams" (svapna).
I don't think that's saying "Nothing exists" -- there's a Zen story about that, quoted here.
Let's parse the phrase in question again, i.e. "the Buddha would argue that there is no such thing as a ‘thing’ - that the concept of an independent, autonomous ‘thing’ is an illusion. "
- I assume that the first clause -- i.e. "there is no such thing as a ‘thing’" -- is a summary of what's explained in the second clause.
- So ignore the first clause (though you seized on it as the title of this topic) and look at the second clause which explains it -- i.e. "the concept of an independent, autonomous ‘thing’ is an illusion."
I think that second clause is saying two things:
- Things aren't really independent and autonomous
- Conceiving them as such is an illusion
I guess that's not very different from the "pratītyasamutpāda" which you described as "just about the idea that all things (assumed to exist) are interdependent".
Your parenthesis -- "(assumed to exist)" -- indicates that what you find surprising is the idea that things might be not assumed to exist.
But it's not talking about "not having existence" -- it's talking about not having Svabhava -- and the original or authoritative sources of that are I think Nāgārjuna and others (which I am not familiar with).
For a different point of view there's this essay -- We are what we think. All that we are arises with our thoughts. With our thoughts we make the world -- which is one of series of analyses of so-called "fake Buddha quotes" by this author. I think he tends to write based on the Pali canon.
Anyway that essay includes (I quote selected extracts),
The essential message is that the qualities of our mind determine whether or not we suffer. There’s nothing in the Pali original that mentions “thoughts” or “the world” at all, never mind that that we are what we think, or that our thoughts create the world.
But didn’t the Buddha himself teach that the world is an illusion? I’m sure some Buddhists believe he did, and the existence of Hindu-Buddhist hybrid texts like Byrom’s Dhammapada is no doubt one reason they do. But while the Buddha said that we have delusion (moha) about the nature of the world, and that we have cognitive distortions (vipallasas) he did not say that the world was an illusion, or māyā — an important term in Hunduism, which is found in the Pali scriptures but only to mean something like “deceit,” “fraud,” “hypocrisy,” etc. He didn’t deny the existence of the world, although he did point out that we make gross errors of interpretation regarding the nature of the world, seeing permanence where there is only change, seeing sources of suffering as sources of joy, and believing there is a separate and permanent self when no such entity does or can exist.
Nor did the Buddha teach the notion that we are what we think.
Perhaps you can find further explanation by searching this site for the "sunyata" tag -- Highest scored 'sunyata' questions.