Thanks!!!!
"alpha blending" was the key word I searched for. mix() seems the esiest way to do that, but It looks a little bit different to the Godot overlay. With the "Porter-Duff-Algorithm" I get exact the same result:
// A over B
vec4 A = texture(texture_map, UV);
vec4 B = texture(TEXTURE, UV);
COLOR.a = A.a + (1.0 - A.a) * B.a;
COLOR.rgb = 1.0 / COLOR.a * (A.a * A.rgb + (1.0 - A.a) * B.a * B.rgb);