### 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.
}
	Ref<InputEventMouse> me = ev;
	if (me.is_valid()) {
		gui.last_mouse_pos = me->get_position();
	}
	if (is_embedding_subwindows() && _sub_windows_forward_input(ev)) {
		set_input_as_handled();
		return;
	}
	if (!_can_consume_input_events()) {
		return;
	}
	if (!is_input_handled()) {
		ERR_FAIL_COND(!is_inside_tree());
		get_tree()->_call_input_pause(input_group, SceneTree::CALL_INPUT_TYPE_INPUT, ev, this); 
	}
	if (!is_input_handled()) {
		ERR_FAIL_COND(!is_inside_tree());
		_gui_input_event(ev);
	} else {
		
		_gui_cleanup_internal_state(ev);
	}
	if (!is_input_handled()) {
		_push_unhandled_input_internal(ev);
	}
	event_count++;
}
#ifndef DISABLE_DEPRECATED
void Viewport::push_unhandled_input(const Ref<InputEvent> &p_event, bool p_local_coords) {