How to bake Sprite2D shader rendered result as texture

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Godot Version

Godot v4.4_beta1

Question

I have a dropdown shadow shader for Sprite2D node for static objects and I use a 2D average pooling to make the edge smooth. The computation increase with the pooling size, so the shader is quite computation expensive. Since the object is static, the shadow is static too so it only need to calculate once. Is there a way to make a texture out of the rendered texture and replace it as the new texture, then disable the shader material?

following is the solution given by Deepseek, but the final_texture is empty. The 2.png is also an empty image.

func bake_texture():
    var original_material = material as ShaderMaterial
    if not original_material:
        return

    var viewport = SubViewport.new()
    viewport.size = texture.get_size()  
    viewport.transparent_bg = true       #
    #viewport.render_target_update_mode = SubViewport.UPDATE_ONCE  
    add_child(viewport)
    
    var sprite_copy = Sprite2D.new()
    sprite_copy.texture = texture
    sprite_copy.material = original_material.duplicate() 
    viewport.add_child(sprite_copy)
    sprite_copy.texture.get_image().save_png("1.png")

    await get_tree().process_frame
        
    var rendered_texture = viewport.get_texture()
    var image = rendered_texture.get_image()
    var final_texture = ImageTexture.create_from_image(image)
    final_texture.get_image().save_png('2.png')

    texture = final_texture
    material = null

    viewport.queue_free()
    baked = true