### 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)

bool _camera_3d_add(Camera3D *p_camera); 
	void _camera_3d_remove(Camera3D *p_camera);
	void _camera_3d_make_next_current(Camera3D *p_exclude);
	void enable_camera_3d_override(bool p_enable);
	bool is_camera_3d_override_enabled() const;
	void set_camera_3d_override_transform(const Transform3D &p_transform);
	Transform3D get_camera_3d_override_transform() const;
	void set_camera_3d_override_perspective(real_t p_fovy_degrees, real_t p_z_near, real_t p_z_far);
	void set_camera_3d_override_orthogonal(real_t p_size, real_t p_z_near, real_t p_z_far);
	void set_disable_3d(bool p_disable);
	bool is_3d_disabled() const;
	Ref<World3D> world_3d;
	Ref<World3D> own_world_3d;
	void set_world_3d(const Ref<World3D> &p_world_3d);
	Ref<World3D> get_world_3d() const;
	Ref<World3D> find_world_3d() const;
	void _own_world_3d_changed();
	void set_use_own_world_3d(bool p_use_own_world_3d);
	bool is_using_own_world_3d() const;
	void _propagate_enter_world_3d(Node *p_node);
	void _propagate_exit_world_3d(Node *p_node);
	void set_use_xr(bool p_use_xr);
	bool is_using_xr();
#endif 
	void _propagate_world_2d_changed(Node *p_node);
	void _validate_property(PropertyInfo &p_property) const;
	Viewport();
	~Viewport();
};
class SubViewport : public Viewport {