### Godot version

v4.1.stable.official [970459615]

### System information

Godot v4.1.stable - Windows 10.0.22621 - Vulkan (Forward+) - dedicated NVIDIA GeForce GTX 1660 Ti (NVIDIA; 31.0.15.3598) - AMD Ryzen 7 3700X 8-Core Processor (16 Threads)

### Issue description

is_input_handled() is returning True, even though set_input_as_handled() has not been called.

Example:
`func _input_event(viewport, event, shape_idx):
	print(viewport.is_input_handled())`

Returns 'True', should return 'False'

### Steps to reproduce

1. Create a new project and add a Node2D as the root
2. Add a child Area2D node containing a CollisionShape2D and a Sprite2D
3. Either create the _input_event(viewport, event, shape_idx) or connect _on_input_event(viewport, event, shape_idx)
4. Print viewport.is_input_handled()
5. True is printed.

### Minimal reproduction project

[input_test.zip](https://github.com/godotengine/godot/files/12063748/input_test.zip)

if (Object::cast_to<InputEventKey>(*p_event) != nullptr || Object::cast_to<InputEventShortcut>(*p_event) != nullptr || Object::cast_to<InputEventJoypadButton>(*p_event) != nullptr) {
		ERR_FAIL_COND(!is_inside_tree());
		get_tree()->_call_input_pause(shortcut_input_group, SceneTree::CALL_INPUT_TYPE_SHORTCUT_INPUT, p_event, this);
	}
	
	if (!is_input_handled()) {
		ERR_FAIL_COND(!is_inside_tree());
		get_tree()->_call_input_pause(unhandled_input_group, SceneTree::CALL_INPUT_TYPE_UNHANDLED_INPUT, p_event, this);
	}
	
	if (!is_input_handled() && (Object::cast_to<InputEventKey>(*p_event) != nullptr)) {
		ERR_FAIL_COND(!is_inside_tree());
		get_tree()->_call_input_pause(unhandled_key_input_group, SceneTree::CALL_INPUT_TYPE_UNHANDLED_KEY_INPUT, p_event, this);
	}
	if (physics_object_picking && !is_input_handled()) {
		if (Input::get_singleton()->get_mouse_mode() != Input::MOUSE_MODE_CAPTURED &&
				(Object::cast_to<InputEventMouse>(*p_event) ||
						Object::cast_to<InputEventScreenDrag>(*p_event) ||
						Object::cast_to<InputEventScreenTouch>(*p_event)
								)) {
			physics_picking_events.push_back(p_event);
			set_input_as_handled();
		}
	}
}
void Viewport::set_physics_object_picking(bool p_enable) {