Dune is like 10,000 years past the Butlerian Jihad which is supposed to be an existential war against AI and humans that leaves Earth unrecognizable. Even generously that's still not even close to this millenia

No. The Butlerian Jihad is somewhere around 10,000 AD, the first book is somewhere around 20k~25k AD.

Also, in my headcannon Dune and 40k are the same universe and the story of Paul Atreades is how the god emperor came to be.

The Humans in Zion think it's closer to 2199, but they don't know about the cycle of The One.

In his cave speech just before the rave, Morpheus says they've been fighting the Machines for 100 years. There are people in Zion old enough that that might be accurate for the cycle they're on.

The Architect says this will be the sixth time they destroy Zion. The Machines being machines are likely consistent in their timeline, which would mean that the cycle of The One takes about 100 years to resolve each time.

So the year is at least 2699, but likely later than that when you take into account the earlier, failed, versions of the Matrix before they figured out The One cycle.

In Matrix the uprisal of the robots happens around the year 2000. I remember a scene though where Morpheus explains to Neo something like "You think the year is 1999, but it's more likely we write the year 2199. We don't know it exactly to be honest".

So this could actually be true

Oh so is that where the 2505 for Dune came from?

Idiocracy's date, which was 2505 according to the newspaper.

A most trustworthy source.