So this website just went up:
https://sjhu.jp/. There's no official English text, but here's what I got after translating it:
We are pleased to announce the launch of "Shin Japan Heroes Universe", a miraculous project in collaboration with the four films "Shin Godzilla", "Shin Evangelion the Movie", "Shin Ultraman" and "Shin Kamen Rider". This project was launched by Toho, Color, Tsuburaya Productions and Toei. The dream collaboration of four of Japan's leading "heroes" has been realized, transcending the boundaries of the companies, because of the connection with the work bearing the name "Shin" in which the rare creator Hideaki Anno participates.
As a start-up, the main visual and emblem of the project have been completed. The visuals were created by Masahiro Maeda and the emblem by Yutaka Debuchi, two people who have a deep connection with each series, and who will add colour to the start of this big project.
We are planning a wide range of events, merchandising and other activities for the future. We will keep you informed on this website.
Stay tuned for Shin Jidai in 2022!
The phrasing in the first paragraph makes it sound like an actual crossover between all four franchises, but the last paragraph leads me to suspect it's most likely going to be something like the Godzilla vs. Evangelion theme park ride rather than a movie.