Vertex snapping shader and transparency

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Godot Version

Godot 4.2

Question

I have the following shader that I’m using for PS1 style vertex snapping. It’s mostly great, but I want to keep the alpha transparency of my textures. If I comment the last line, the geometry messes up and I can see through faces. How do I prevent that?

shader_type spatial;

uniform sampler2D albedo_texture : source_color, filter_nearest;
uniform vec4 tint_color = vec4(1.0, 0.0, 0.0, 1.0);

void vertex() {
    float snap_value = 1.0 / 200.0;
    vec4 clip_pos = PROJECTION_MATRIX * MODELVIEW_MATRIX * vec4(VERTEX, 1.0);
    vec3 ndc_pos = clip_pos.xyz / clip_pos.w;
    ndc_pos.xy = floor(ndc_pos.xy / snap_value + 0.5) * snap_value;
    clip_pos.xyz = ndc_pos * clip_pos.w;
    POSITION = clip_pos;
}

void fragment() {
    vec4 tex_color = texture(albedo_texture, UV);
    ALBEDO = tex_color.rgb * tint_color.rgb;
    //ALPHA = tex_color.a;
}