I'm rather reluctant to call this an April Fools joke. Usually, Japanese companies are super incredibly clear about labelling stuff as an April 1 gag. This hit earlier today (still April Fools in Japan), appearing on the official Evangelion site as the "most maximum collaboration of 2016". So, that's what it is, really. A tie-up between two different properties, which happens all the time in Japan and elsewhere.
The subsite on the official page for the upcoming Shin Godzilla movie even has Evangelion x Godzilla goods for sale, which will be out starting later this month and continuing through June. So yeah, that's long after April Fools' Day is over, and this is way too normal to be a joke.
The lead art is done by veteran animator and character designer Mahiro Maeda, who is currently working on the new Godzilla film. Among his many illustrious credits, he cut his teeth working on classic anime like Nausicaä of the Valley of the Wind. Know who else worked on that? Shin Godzilla director Hideaki Anno, who is probably best known as Evangelion's creator.
See? The tie-up all makes sense, and this is more fan service than April Fools.