### 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
ScriptLanguage::CodeCompletionOption option(*kw, ScriptLanguage::CODE_COMPLETION_KIND_PLAIN_TEXT);
		r_result.insert(option.display, option);
		kw++;
	}
	static const char *_keywords_with_space[] = {
		"and", "not", "or", "in", "as", "class", "class_name", "extends", "is", "func", "signal", "await",
		"const", "enum", "static", "var", "if", "elif", "else", "for", "match", "when", "while",
		nullptr
	};
	const char **kws = _keywords_with_space;
	while (*kws) {
		ScriptLanguage::CodeCompletionOption option(*kws, ScriptLanguage::CODE_COMPLETION_KIND_PLAIN_TEXT);
		option.insert_text += " ";
		r_result.insert(option.display, option);
		kws++;
	}
	static const char *_keywords_with_args[] = {
		"assert", "preload",
		nullptr
	};
	const char **kwa = _keywords_with_args;
	while (*kwa) {
		ScriptLanguage::CodeCompletionOption option(*kwa, ScriptLanguage::CODE_COMPLETION_KIND_FUNCTION);
		option.insert_text += "(";
		r_result.insert(option.display, option);
		kwa++;
	}
	List<StringName> utility_func_names;
	Variant::get_utility_function_list(&utility_func_names);
	for (List<StringName>::Element *E = utility_func_names.front(); E; E = E->next()) {