### 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)

first = E;
					}
				}
				if (first) {
					first->make_current();
				}
			}
#endif 
		} break;
		case NOTIFICATION_EXIT_TREE: {
			_gui_cancel_tooltip();
			RenderingServer::get_singleton()->viewport_set_scenario(viewport, RID());
			RenderingServer::get_singleton()->viewport_remove_canvas(viewport, current_canvas);
			if (contact_2d_debug.is_valid()) {
				RenderingServer::get_singleton()->free(contact_2d_debug);
				contact_2d_debug = RID();
			}
			if (contact_3d_debug_multimesh.is_valid()) {
				RenderingServer::get_singleton()->free(contact_3d_debug_multimesh);
				RenderingServer::get_singleton()->free(contact_3d_debug_instance);
				contact_3d_debug_instance = RID();
				contact_3d_debug_multimesh = RID();
			}
			remove_from_group("_viewports");
			set_physics_process_internal(false);
			RS::get_singleton()->viewport_set_active(viewport, false);
			RenderingServer::get_singleton()->viewport_set_parent_viewport(viewport, RID());
		} break;
		case NOTIFICATION_PATH_RENAMED: {
			_update_viewport_path();