How to implement pursuit in UNITY, but only along the X and Z axes?

Question

C++ / C#

Hello. I understand that the question is very complex and I, in fact, just ask you to write a script for me, but I'm a little stumped. Making the enemy follow you is not a problem when he runs in a straight line like in 3d games, but my project should be limited like it's a 16 bit game from the last century and nothing comes to my mind, maybe you are some guide advise? Thanks in advance.
Here is a gif from a guide on another engine how it should look.

Answer 1

Do pseudo2d - the easiest option, originally Unity 3d engine and even when you create a 2d project, there is almost the same processing as 3d. So:
You create a 3D project, switch the camera to 2D, turn the "ground" to face the camera, then put obstacles from cubes "conditionally" on it. You create a character, make it control with movement only along the 2 necessary axes, throw a 2D sprite on it. And you set up bots through the standard NavMesh and voila, you have a 2D game with 3D capabilities.