### 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
#ifdef TOOLS_ENABLED
	if (Engine::get_singleton()->is_editor_hint()) {
		bool use_space_indentation = EDITOR_GET("text_editor/behavior/indent/type");
		if (use_space_indentation) {
			int indent_size = EDITOR_GET("text_editor/behavior/indent/size");
			return String(" ").repeat(indent_size);
		}
	}
#endif
	return "\t";
}
void GDScriptLanguage::auto_indent_code(String &p_code, int p_from_line, int p_to_line) const {
	String indent = _get_indentation();
	Vector<String> lines = p_code.split("\n");
	List<int> indent_stack;
	for (int i = 0; i < lines.size(); i++) {
		String l = lines[i];
		int tc = 0;
		for (int j = 0; j < l.length(); j++) {
			if (l[j] == ' ' || l[j] == '\t') {
				tc++;
			} else {
				break;
			}
		}
		String st = l.substr(tc, l.length()).strip_edges();
		if (st.is_empty() || st.begins_with("#")) {
			continue; 
		}
		int ilevel = 0;