### 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
return EditorNode::get_singleton()->get_edited_scene();
}
void EditorNode::_print_handler(void *p_this, const String &p_string, bool p_error, bool p_rich) {
	callable_mp_static(&EditorNode::_print_handler_impl).bind(p_string, p_error, p_rich).call_deferred();
}
void EditorNode::_print_handler_impl(const String &p_string, bool p_error, bool p_rich) {
	if (!singleton) {
		return;
	}
	if (p_error) {
		singleton->log->add_message(p_string, EditorLog::MSG_TYPE_ERROR);
	} else if (p_rich) {
		singleton->log->add_message(p_string, EditorLog::MSG_TYPE_STD_RICH);
	} else {
		singleton->log->add_message(p_string, EditorLog::MSG_TYPE_STD);
	}
}
static void _execute_thread(void *p_ud) {