### Godot version

4.1.1

### System information

windows 11

### Issue description

When registering a type with class_name and using that class name to declare a variable in code only, autocomplete works as expected anywhere in other nodes/scenes. However, if making a custom scene node that extends a script with the class_name, if that custom scene is instantiated in a different scene, even if the type is specified, it only shows the parent node's functions and not any of the extended functionality. I have made a basic project showing the issue

### Steps to reproduce

I have made a very simple project showing the issue. https://github.com/mmmmmmmmmmmmmmmmmmmdonuts/godot_4_autocomplete_issue essentially, the extended Node scene will only show the custom function when both the type is specified as well as the type afterwards following "as" 
e.g. `@onready var my_class_4: MyClass = $MyClass4 as MyClass`

### Minimal reproduction project

https://github.com/mmmmmmmmmmmmmmmmmmmdonuts/godot_4_autocomplete_issue
if (_debug_parse_err_line >= 0) {
		return nullptr;
	}
	ERR_FAIL_INDEX_V(p_level, _call_stack.stack_pos, nullptr);
	int l = _call_stack.stack_pos - p_level - 1;
	ScriptInstance *instance = _call_stack.levels[l].instance;
	return instance;
}
void GDScriptLanguage::debug_get_globals(List<String> *p_globals, List<Variant> *p_values, int p_max_subitems, int p_max_depth) {
	const HashMap<StringName, int> &name_idx = GDScriptLanguage::get_singleton()->get_global_map();
	const Variant *gl_array = GDScriptLanguage::get_singleton()->get_global_array();
	List<Pair<String, Variant>> cinfo;
	get_public_constants(&cinfo);
	for (const KeyValue<StringName, int> &E : name_idx) {
		if (ClassDB::class_exists(E.key) || Engine::get_singleton()->has_singleton(E.key)) {
			continue;
		}
		bool is_script_constant = false;