### 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 (!vp) {
		if (!vp_pending) {
			ERR_PRINT("Viewport Texture must be set to use it.");
		}
		return Ref<Image>();
	}
	return RS::get_singleton()->texture_2d_get(vp->texture_rid);
}
void ViewportTexture::_setup_local_to_scene(const Node *p_loc_scene) {
	
	vp_pending = false;
	Node *vpn = p_loc_scene->get_node_or_null(path);
	ERR_FAIL_NULL_MSG(vpn, "Path to node is invalid: '" + path + "'.");
	vp = Object::cast_to<Viewport>(vpn);
	ERR_FAIL_NULL_MSG(vp, "Path to node does not point to a viewport: '" + path + "'.");
	vp->viewport_textures.insert(this);
	ERR_FAIL_NULL(RenderingServer::get_singleton());
	if (proxy_ph.is_valid()) {
		RS::get_singleton()->texture_proxy_update(proxy, vp->texture_rid);
		RS::get_singleton()->free(proxy_ph);
		proxy_ph = RID();
	} else {
		ERR_FAIL_COND(proxy.is_valid()); 
		proxy = RS::get_singleton()->texture_proxy_create(vp->texture_rid);
	}
	vp_changed = false;
	emit_changed();
}
void ViewportTexture::_bind_methods() {