### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
ERR_FAIL_NULL(p_dock);
	Size2 borders = Size2(4, 4) * EDSCALE;
	
	Size2 dock_size = p_dock->get_size() + borders * 2;
	Point2 dock_screen_pos = p_dock->get_screen_position();
	int dock_index = p_dock->get_index() - 1;
	dock_slot[p_slot_index]->remove_child(p_dock);
	WindowWrapper *wrapper = memnew(WindowWrapper);
	wrapper->set_window_title(vformat(TTR("%s - Godot Engine"), p_dock->get_name()));
	wrapper->set_margins_enabled(true);
	gui_base->add_child(wrapper);
	wrapper->set_wrapped_control(p_dock);
	wrapper->set_meta("dock_slot", p_slot_index);
	wrapper->set_meta("dock_index", dock_index);
	wrapper->set_meta("dock_name", p_dock->get_name().operator String());
	p_dock->show();
	wrapper->connect("window_close_requested", callable_mp(this, &EditorNode::_dock_floating_close_request).bind(wrapper));
	dock_select_popup->hide();
	if (p_show_window) {
		wrapper->restore_window(Rect2i(dock_screen_pos, dock_size), get_window()->get_current_screen());
	}
	_update_dock_slots_visibility(true);
	floating_docks.push_back(wrapper);
	_edit_current();
}
void EditorNode::_dock_select_input(const Ref<InputEvent> &p_input) {