No, Phoenix Point is not a new Phoenix Wright game. While it would be awesome if there was a new game that featured the legendary attorney fighting aliens, what Phoenix Point is, is good enough.
Helmed by the original creator of Xcom, Julian Gallop, this new turn-based strategy will certainly feel like a walk down memory lane. While the game cant be a direct successor to that series, it even feels like it should exist in the same universe.
Source: N4G PC Phoenix Point Review: Out of This World Improvement on X-Com| The Nerd Stash