I was under the impression that SE used an extremely modified (to the point where it is no longer Crystal Tools) version as the basis for the ARR engine.

The Luminous Engine, as far as I can tell, was used for Final Fantasy XV and ... Forspoken?

No confirmations about Final Fantasy XVI's engine, but it is definitely not the FFXIV engine, nor Luminous. According to the title of an article on cgworld.jp in 2023, 独自エンジンによる、アートとリアルの中間をねらった画づくり〜『FINAL FANTASY XVI』（1） 開発環境・画づくり篇 ... (key words being "proprietary engine" and "development environment).

Autotranslate in Edge provides: In addition, this game is developed with a newly designed in-house engine. Mr. Honda explains, "Considering the man-hours required for support when using a general-purpose game engine or an in-house engine, it was more suitable to develop and manage it ourselves from scratch."

[Source: https://cgworld.jp/article/202309-cgw301-ff16-01.html ]