is there a way to make particles face the player in one axis but stay at a specific direction in another axis?

Set the rotation on tick to face the nearest player using an angle equation but only with a custom entity

Potentially possible to do this using the set rotation of particle procedure, you get the angle between the x z of the particle and the x z of the player. Get the nearest player or use some sort of client side assignment to select the correct players x z, depends if you want it to work the same on multiplayer

Also try doing that in client side because thats unnecessary work for the server