I think the issue is the shader is not taking the image's alpha into account, which is why the image is all black.
I made a few adjustments, and while I have not tested it, I believe the shader should now take the alpha of the image into account, while also working with the progress range.
shader_type spatial;
uniform sampler2D texture_albedo : hint_albedo;
uniform float progress: hint_range(0, 1);
void fragment()
{
vec4 albedo_tex = texture(texture_albedo, UV);
ALBEDO = albedo_tex.rgb;
ALPHA = albedo_tex.a;
// May need to be flipped. I do not remember if UVs start at 1 or 0...
if (UV.x > progress)
{
ALPHA = 0;
}
}