Question Painting shader dark edges issue

Hello,
I am making a drawing mini-game and I am currently trying to create a paint shader.
I use a white transparent image for the brush, for example:

In this case, I added a black background, but in Unity, I have imported the same texture without the background. This brush image is premultiplied by me in a separate shader as such:

Code (CSharp):

1. fixed4 frag(v2f i) : SV_Target
2. {
3.     fixed4 color = tex2D(_MainTex, i.uv);
4.  
5.     fixed alpha = color.w;
6.     color.x *= alpha;
7.     color.y *= alpha;
8.     color.z *= alpha;
9.  
10.     return color;
11. }

And then in the painting shader, I do this:

Code (CSharp):

1. fixed4 frag(v2f i) : SV_Target
2. {
3.     fixed4 mask = tex2D(_MainTex, i.uv) /* The brush texture */ * _Color;
4.     fixed4 backdrop = tex2D(_Backdrop, i.bguv); //The painting canvas texture
5.  
6.     fixed4 color = backdrop * (1 - mask.a) + mask;
7.     return color;
8. }

However, the output is not great...
(The checker grid in the background is just a separate image with a grid background that indicates transparency and then I have another image in front that is painting result texture)



Can someone help me understand why is this happening? Thank you