Extensive work on virtually all of the visuals and the net code

visuals/shaders/intersection.gdshader

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+shader_type spatial;
+render_mode blend_add, cull_disabled;
+
+uniform vec4 intersection_color : source_color = vec4(1.0, 0.5, 0.0, 1.0);
+uniform float intersection_thickness = 0.5;
+uniform float intensity = 1.0f;
+uniform sampler2D DEPTH_TEXTURE : hint_depth_texture, filter_linear_mipmap;
+
+void fragment() {
+    // 1. Get linear depth of the scene (opaque objects)
+    float depth = texture(DEPTH_TEXTURE, SCREEN_UV).x;
+    vec3 ndc = vec3(SCREEN_UV * 2.0 - 1.0, depth);
+    vec4 view = INV_PROJECTION_MATRIX * vec4(ndc, 1.0);
+    view.xyz /= view.w;
+    float linear_depth = -view.z;
+
+    // 2. Get linear depth of the current object
+    float linear_frag_coord = -VERTEX.z;
+
+    // 3. Calculate difference
+    float diff = linear_depth - linear_frag_coord;
+
+    // 4. Create intersection mask
+    float intersect = clamp(diff / intersection_thickness, 0.0, 1.0);
+
+    // Invert so the intersection is 1.0
+    intersect = 1.0 - intersect;
+
+    // Output color
+    float strength = .25 + .75 * (1.0 + sin(TIME*3.0))/2.0;
+
+    ALPHA = max(.05, intersect * intersection_color.a * strength);
+	if(ALPHA == .05){
+		ALBEDO = intersection_color.rgb;
+	}else{
+		ALBEDO = intersection_color.rgb * strength;
+		EMISSION = intersection_color.rgb * intensity * strength; // Glow effect
+	}
+
+}