### 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)

ERR_READ_THREAD_GUARD_V(false);
	return gui.dragging;
}
bool Viewport::gui_is_drag_successful() const {
	ERR_READ_THREAD_GUARD_V(false);
	return gui.drag_successful;
}
void Viewport::set_input_as_handled() {
	ERR_MAIN_THREAD_GUARD;
	if (!handle_input_locally) {
		ERR_FAIL_COND(!is_inside_tree());
		Viewport *vp = this;
		while (true) {
			if (Object::cast_to<Window>(vp)) {
				break;
			}
			if (!vp->get_parent()) {
				break;
			}
			vp = vp->get_parent()->get_viewport();
		}
		if (vp != this) {
			vp->set_input_as_handled();
			return;
		}
	}
	local_input_handled = true;
}
bool Viewport::is_input_handled() const {