This is laughably wrong. Upanishads are part of the Vedas in context and as part of a larger contextual work..then expounded separately by several authors...no one knows who or how many people wrote the Vedas.
There is literally no proof either way. Just like no one can prove the authorship of vedas or Upanishads, there is no way to prove that they are ‘entirely distinct works of literature’.
Upanishads are not fungible and are married to specific related Veda. What you say doesn’t even make basic sense.
For example: Brihadaranyaka Upanishad is related to Yajur Veda and so it’s distinctly expounding upon Shukla YajurVeda. It makes no sense with Rig or Atharva or Sama Veda. So it is part of Yajur Veda.
The Vedas were orally transmitted as the language of the Brahmins and then written down much much later.
You can’t date or confer authorship on Vedas or Upanishads, but the commentaries and exposition are codified wrt the four vedas and each Upanishads is assigned to one of the four.
There is literally no basis for you to assert that ‘they are distinct works of literature’.
However: Without Vedas, Upanishads are not stand alone works. Vedas, otoh are relevant and understood without the Upanishads.
> Upanishads are the later chapters of the Vedas.
They are not later chapters of the Vedas. They are entirely distinct works of literature.