### Godot version

4.0.3-stable

### System information

Windows 10

### Issue description

In some projects ViewportTexture remains pink and doesn't render viewport content after upgrading from 4.0.2-stable to 4.0.3-stable. If a pair of files viewport.h/viewport.cpp are downgraded back to what they were in 4.0.2-stable, problem goes away.

This is how it looks in 4.0.3-stable:
![4 0 3_stable_viewport_4 0 3](https://github.com/godotengine/godot/assets/1449921/44c191a9-4b67-4b02-90b6-4ab615f62a73)

And this is how it looks if viewport.h/viewport.cpp are downgraded back to what they were in 4.0.2-stable.
![4 0 3_stable_viewport_4 0 2](https://github.com/godotengine/godot/assets/1449921/f5abc605-f129-4222-9c0e-e9a07621dd9d)



### Steps to reproduce

Unfortunately, I cannot come up wit a simple demo project reproducing the problem. It exists in some projects and doesn't exist in others.


### Minimal reproduction project

Cannot produce a simple project reproducing the problem. In simple projects it works fine.
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;
		}
	}