### Godot version

v4.1.dev.custom_build [18112ba36]

### System information

Linux Mint 21.1, NVIDIA GeForce GTX 1050 Ti,  Vulkan API 1.3.205

### Issue description

This is a regression from #64388. 

Textures seem to be used differently in 2D and 3D. They are rendered using the `RID` in 3D, and changing the `viewport_path` will cause the `RID` to change.

https://github.com/godotengine/godot/assets/30386067/ad393fe8-50c1-4a89-870d-58d4e224bcc6


### Steps to reproduce

1. Download and import MRP.
2. Open 1.tscn, and try to switch the `viewport_path` of the `MeshInstance3D:mesh:material:albedo_texture` in the MeshInstance3D node.
3. After switching, the MeshInstance3D is rendered as white in the editor;
4. Close and then reopen 1.tscn.

### Minimal reproduction project

[ViewportTexture-change-viewport_path.zip](https://github.com/godotengine/godot/files/11509010/ViewportTexture-change-viewport_path.zip)

if (p_node != this) {
		Window *w = Object::cast_to<Window>(p_node);
		if (w && (!w->is_inside_tree() || !w->is_embedded())) {
			return;
		}
		CanvasItem *ci = Object::cast_to<CanvasItem>(p_node);
		if (ci) {
			ci->queue_redraw();
		}
	}
	int cc = p_node->get_child_count();
	for (int i = 0; i < cc; i++) {
		_update_canvas_items(p_node->get_child(i));
	}
}
Ref<ViewportTexture> Viewport::get_texture() const {
	ERR_READ_THREAD_GUARD_V(Ref<ViewportTexture>());
	return default_texture;
}
void Viewport::set_positional_shadow_atlas_size(int p_size) {
	ERR_MAIN_THREAD_GUARD;
	positional_shadow_atlas_size = p_size;
	RS::get_singleton()->viewport_set_positional_shadow_atlas_size(viewport, p_size, positional_shadow_atlas_16_bits);
}
int Viewport::get_positional_shadow_atlas_size() const {