Here is the correct naming convention for the series you actually want to watch:

Does it refer to a limited-edition wristwatch from the anime? Is it a secret director’s cut? Or is it simply a typo spreading through streaming forums?

So, why are thousands of people searching for "Evangelion 111 watch"?

The Typo Theory: 1.11, 2.22, 3.33, and 3.0+1.01 The "111" is a misremembered or typo-laden version of the film’s versioning system. Unlike standard sequels (Part 1, Part 2, Part 3), the Rebuild movies use decimal points to denote home video releases and refinements.