My terrain has a vertex shader, but my terrain tree doesn't interact along with it!

I have a terrain, and I have a tree object on that terrain.
This is what I want:

My GOAL is to have the plane to bend and the environment objects follow.

More info below!

This is what Im getting:

The reason it’s bending as shown below…

is because I have a shader applied.

Based on my visuals, My GOAL is to have the plane to bend and the environment objects follow.

My shader is from this interactive rug video. You can check it out if you’d like. I’m unsure if this extra comment matter at all, but I also set a “transform_position” empty object into my project and attached a really simple script, just like the video, that places where the bending will happen on the plane.

ANYWAY Anyway, if you’re too lazy to look at the video, here’s my shader for my terrain and my script attached to the “transform_position” obj that places the bending on the plane.

using UnityEngine;

public class objectPosition : MonoBehaviour
{
 
    void Update()
    {
        Shader.SetGlobalVector("position", new Vector3(this.transform.position.x, this.transform.position.y, this.transform.position.z));
    }
}

I’m not sure what else I need to include, but I’m open to learn new things. I’m pretty much beginner. Maybe it has something to do with recasting, or gpu or cpu?? Those are just terms I came across when I was trying to find answers this week haha. So please help! This is my first time doing the unity discussion so please be kind!