### 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 (!is_inside_tree()) {
		return;
	}
	if (!physics_object_picking) {
		return;
	}
	if (Object::cast_to<Window>(this) && Input::get_singleton()->get_mouse_mode() == Input::MOUSE_MODE_CAPTURED) {
		return;
	}
	if (!gui.mouse_in_viewport) {
		
		physics_picking_events.clear();
		return;
	}
	_drop_physics_mouseover(true);
#ifndef _3D_DISABLED
	Vector2 last_pos(1e20, 1e20);
	CollisionObject3D *last_object = nullptr;
	ObjectID last_id;
	PhysicsDirectSpaceState3D::RayResult result;
#endif 
	PhysicsDirectSpaceState2D *ss2d = PhysicsServer2D::get_singleton()->space_get_direct_state(find_world_2d()->get_space());
	bool has_mouse_event = false;
	for (const Ref<InputEvent> &e : physics_picking_events) {
		Ref<InputEventMouse> m = e;
		if (m.is_valid()) {
			has_mouse_event = true;
			break;
		}
	}