### Godot version

v4.2.rc.mono.custom_build [ad72de508]

### System information

Windows 10

### Issue description

As I pointed out several times earlier in [#80284](https://github.com/godotengine/godot/pull/80284#issuecomment-1722120503), the references to singletons in `GDScript` are still not updated after the `GDExtension` reload.

https://github.com/godotengine/godot/assets/7782218/f90052a5-0de2-4310-8235-f0b9e2f74b3a

Singletons themselves are updated and work correctly, but references to these singletons are not updated in `@tool` scripts. That is, `Engine.get_singleton` returns the actual working reference, but using the singleton directly through its name causes errors.

### Steps to reproduce

* Clone `4.2.reload_singleton` branch from the MRP repository https://github.com/DmitriySalnikov/gde_test_cases/tree/4.2.reload_singleton
* Build as usual
* Open the project from the `project/` folder
* Add one character to the source code and rebuild
* Focus on the editor to reload extension
* Watch for error spam when calling by singleton name

### Minimal reproduction project

https://github.com/DmitriySalnikov/gde_test_cases/tree/4.2.reload_singleton
if (is_built_in() && !get_name().is_empty()) {
		return vformat("%s(%s)", get_name(), get_script_path());
	} else {
		return get_script_path();
	}
}
Error GDScript::_static_init() {
	if (static_initializer) {
		Callable::CallError call_err;
		static_initializer->call(nullptr, nullptr, 0, call_err);
		if (call_err.error != Callable::CallError::CALL_OK) {
			return ERR_CANT_CREATE;
		}
	}
	Error err = OK;
	for (KeyValue<StringName, Ref<GDScript>> &inner : subclasses) {
		err = inner.value->_static_init();
		if (err) {
			break;
		}
	}
	return err;
}
#ifdef TOOLS_ENABLED
void GDScript::_save_old_static_data() {