### 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)

capture_object = Object::cast_to<CollisionObject3D>(ObjectDB::get_instance(physics_object_capture));
			if (!capture_object || !camera_3d || (mb.is_valid() && mb->get_button_index() == MouseButton::LEFT && !mb->is_pressed())) {
				physics_object_capture = ObjectID();
			}
		}
		if (pos == last_pos) {
			if (last_id.is_valid()) {
				if (ObjectDB::get_instance(last_id) && last_object) {
					
					_collision_object_3d_input_event(last_object, camera_3d, ev, result.position, result.normal, result.shape);
					if (last_object->get_capture_input_on_drag() && mb.is_valid() && mb->get_button_index() == MouseButton::LEFT && mb->is_pressed()) {
						physics_object_capture = last_id;
					}
				}
			}
		} else {
			if (camera_3d) {
				Vector3 from = camera_3d->project_ray_origin(pos);
				Vector3 dir = camera_3d->project_ray_normal(pos);
				real_t far = camera_3d->far;
				PhysicsDirectSpaceState3D *space = PhysicsServer3D::get_singleton()->space_get_direct_state(find_world_3d()->get_space());
				if (space) {
					PhysicsDirectSpaceState3D::RayParameters ray_params;
					ray_params.from = from;
					ray_params.to = from + dir * far;
					ray_params.collide_with_areas = true;
					ray_params.pick_ray = true;
					bool col = space->intersect_ray(ray_params, result);
					ObjectID new_collider;
					CollisionObject3D *co = col ? Object::cast_to<CollisionObject3D>(result.collider) : nullptr;