### 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)

panel->set_theme_type_variation(SNAME("TooltipPanel"));
	
	
	Control *base_tooltip = tooltip_owner->make_custom_tooltip(tooltip_text);
	
	if (!base_tooltip) {
		gui.tooltip_label = memnew(Label);
		gui.tooltip_label->set_theme_type_variation(SNAME("TooltipLabel"));
		gui.tooltip_label->set_auto_translate(gui.tooltip_control->is_auto_translating());
		gui.tooltip_label->set_text(tooltip_text);
		base_tooltip = gui.tooltip_label;
		panel->connect("mouse_entered", callable_mp(this, &Viewport::_gui_cancel_tooltip));
	}
	base_tooltip->set_anchors_and_offsets_preset(Control::PRESET_FULL_RECT);
	panel->set_transient(true);
	panel->set_flag(Window::FLAG_NO_FOCUS, true);
	panel->set_flag(Window::FLAG_POPUP, false);
	panel->set_flag(Window::FLAG_MOUSE_PASSTHROUGH, true);
	panel->set_wrap_controls(true);
	panel->add_child(base_tooltip);
	panel->gui_parent = this;
	gui.tooltip_popup = panel;
	tooltip_owner->add_child(gui.tooltip_popup);
	Point2 tooltip_offset = GLOBAL_GET("display/mouse_cursor/tooltip_position_offset");
	Rect2 r(gui.tooltip_pos + tooltip_offset, gui.tooltip_popup->get_contents_minimum_size());
	r.size = r.size.min(panel->get_max_size());
	Window *window = gui.tooltip_popup->get_parent_visible_window();
	Rect2i vr;
	if (gui.tooltip_popup->is_embedded()) {
		vr = gui.tooltip_popup->get_embedder()->get_visible_rect();