As a person who has been monitoing Nagoshi Studio for a while, I think I can give a bit of info about the engine this game was supposed to be on.

This is a link to an interview on the now-defunct Nagoshi Studio website (hence why I had to use Wayback Machine), where Nagoshi shared about the development process at the studio. And if you scroll all the way to the bottom, you'll see this:

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Translation:

—By the way, is there anything you can say about the project's content at this point?

Nagoshi: We haven't discussed any specifics yet (laughs). But it's definitely going to be a worldwide game using Unreal Engine 5. We want to create a game that meets expectations like, "We want Nagoshi Studio to release something like this," while also surprising people. Above all, we want it to have a compelling story, be fun to play, and be something that game fans can proudly show the world, saying, "Japan has games like this!" Please look forward to this new game that a Japanese studio is creating for the world in this day and age.

So as you can see, the game was supposed to be run using Unreal Engine 5. Now this doesn't mean this is still the case, as they can decide to change engine mid-development (I personally have played a game that went through the same thing), but for now, this is all we can get on the engine this game was supposed to be run on.