### 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 (mm.is_valid()) {
			if (gui.subwindow_drag == SUB_WINDOW_DRAG_MOVE) {
				Vector2 diff = mm->get_position() - gui.subwindow_drag_from;
				Rect2i new_rect(gui.subwindow_drag_pos + diff, gui.currently_dragged_subwindow->get_size());
				if (gui.currently_dragged_subwindow->is_clamped_to_embedder()) {
					new_rect = gui.currently_dragged_subwindow->fit_rect_in_parent(new_rect, get_visible_rect());
				}
				gui.currently_dragged_subwindow->_rect_changed_callback(new_rect);
				if (DisplayServer::get_singleton()->has_feature(DisplayServer::FEATURE_CURSOR_SHAPE)) {
					DisplayServer::get_singleton()->cursor_set_shape(DisplayServer::CURSOR_MOVE);
				}
			}
			if (gui.subwindow_drag == SUB_WINDOW_DRAG_CLOSE) {
				gui.subwindow_drag_close_inside = gui.subwindow_drag_close_rect.has_point(mm->get_position());
			}
			if (gui.subwindow_drag == SUB_WINDOW_DRAG_RESIZE) {
				Vector2i diff = mm->get_position() - gui.subwindow_drag_from;
				Size2i min_size = gui.currently_dragged_subwindow->get_min_size();
				Size2i min_size_clamped = gui.currently_dragged_subwindow->get_clamped_minimum_size();
				min_size_clamped.x = MAX(min_size_clamped.x, 1);
				min_size_clamped.y = MAX(min_size_clamped.y, 1);
				Rect2i r = gui.subwindow_resize_from_rect;
				Size2i limit = r.size - min_size_clamped;
				switch (gui.subwindow_resize_mode) {
					case SUB_WINDOW_RESIZE_TOP_LEFT: {
						diff.x = MIN(diff.x, limit.x);
						diff.y = MIN(diff.y, limit.y);
						r.position += diff;
						r.size -= diff;
					} break;