Surface Shader vertex displacement, shadows not moving

I've got a surface shader where the vertices are slightly moving over time but somehow the shadows aren't changing correctly according to the new vertex positions. I thought about a custom shadow pass where i also displace the vertices but how would i do that with a surface shader?

 Shader "Custom/leaf" {
     Properties{
         _Color("Color", Color) = (1,1,1,1)
         _MainTex("Albedo (RGB)", 2D) = "white" {}
         _Glossiness("Smoothness", Range(0,1)) = 0.5
         _Metallic("Metallic", Range(0,1)) = 0.0
     }
     
     SubShader {
         Tags { "Queue" = "Transparent" "RenderType" = "Transparent" }
         LOD 200
         //Blend SrcAlpha OneMinusSrcAlpha
         CGPROGRAM
         // Physically based Standard lighting model, and enable shadows on all light types
         #pragma surface surf Standard vertex:vert alpha:fade
 
         // Use shader model 3.0 target, to get nicer looking lighting
         #pragma target 3.0 
 
         void vert(inout appdata_full v) {
             float3 worldPos = mul(unity_ObjectToWorld, v.vertex).xyz;
             float m = sin(_Time.z * 2 + worldPos.x + worldPos.y + worldPos.z);
             v.vertex.y += m * v.texcoord.x*0.02;
             v.vertex.xz += m * worldPos.y*0.001;
         }
 
         sampler2D _MainTex;
         half _Glossiness;
         half _Metallic;
         fixed4 _Color;
 
         struct Input {
             float2 uv_MainTex;
         };
 
         void surf(Input IN, inout SurfaceOutputStandard o) {
             fixed4 c = tex2D(_MainTex, IN.uv_MainTex) * _Color;
             o.Albedo = c.rgb;
             o.Metallic = _Metallic;
             o.Smoothness = _Glossiness;
             o.Alpha = c.a;
         }
 
     ENDCG
     }
     
     Fallback "Transparent/Cutout/Diffuse"
 }