### 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(SDF_SCALE_100_PERCENT);
	return sdf_scale;
}
Transform2D Viewport::get_screen_transform() const {
	ERR_READ_THREAD_GUARD_V(Transform2D());
	return get_screen_transform_internal();
}
Transform2D Viewport::get_screen_transform_internal(bool p_absolute_position) const {
	ERR_READ_THREAD_GUARD_V(Transform2D());
	return get_final_transform();
}
void Viewport::update_mouse_cursor_state() {
	
	Window *base_window = get_base_window();
	if (base_window) {
		base_window->update_mouse_cursor_state();
	}
}
void Viewport::set_canvas_cull_mask(uint32_t p_canvas_cull_mask) {
	ERR_MAIN_THREAD_GUARD;
	canvas_cull_mask = p_canvas_cull_mask;
	RenderingServer::get_singleton()->viewport_set_canvas_cull_mask(viewport, canvas_cull_mask);
}
uint32_t Viewport::get_canvas_cull_mask() const {
	ERR_READ_THREAD_GUARD_V(0);
	return canvas_cull_mask;
}
void Viewport::set_canvas_cull_mask_bit(uint32_t p_layer, bool p_enable) {