### 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 (co && co->can_process()) {
						new_collider = result.collider_id;
						if (!capture_object) {
							last_object = co;
							last_id = result.collider_id;
							if (co->get_capture_input_on_drag() && mb.is_valid() && mb->get_button_index() == MouseButton::LEFT && mb->is_pressed()) {
								physics_object_capture = last_id;
							}
						}
					}
					if (is_mouse && new_collider != physics_object_over) {
						if (physics_object_over.is_valid()) {
							CollisionObject3D *previous_co = Object::cast_to<CollisionObject3D>(ObjectDB::get_instance(physics_object_over));
							if (previous_co) {
								previous_co->_mouse_exit();
							}
						}
						if (new_collider.is_valid()) {
							DEV_ASSERT(co);
							co->_mouse_enter();
						}
						physics_object_over = new_collider;
					}
					if (capture_object) {
						_collision_object_3d_input_event(capture_object, camera_3d, ev, result.position, result.normal, result.shape);
					} else if (new_collider.is_valid()) {
						_collision_object_3d_input_event(co, camera_3d, ev, result.position, result.normal, result.shape);
					}
				}
				last_pos = pos;