### 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
.replace(": Array[String]", "")
									 .replace(": Node", "")
									 .replace(": CharFXTransform", "")
									 .replace(":=", "=")
									 .replace(" -> void", "")
									 .replace(" -> bool", "")
									 .replace(" -> int", "")
									 .replace(" -> PortType", "")
									 .replace(" -> String", "")
									 .replace(" -> Object", "");
	}
	processed_template = processed_template.replace("_BASE_", p_base_class_name)
								 .replace("_CLASS_SNAKE_CASE_", p_class_name.to_snake_case().validate_identifier())
								 .replace("_CLASS_", p_class_name.to_pascal_case().validate_identifier())
								 .replace("_TS_", _get_indentation());
	scr->set_source_code(processed_template);
	return scr;
}
Vector<ScriptLanguage::ScriptTemplate> GDScriptLanguage::get_built_in_templates(StringName p_object) {
	Vector<ScriptLanguage::ScriptTemplate> templates;
#ifdef TOOLS_ENABLED
	for (int i = 0; i < TEMPLATES_ARRAY_SIZE; i++) {
		if (TEMPLATES[i].inherit == p_object) {
			templates.append(TEMPLATES[i]);
		}
	}
#endif
	return templates;
}
static void get_function_names_recursively(const GDScriptParser::ClassNode *p_class, const String &p_prefix, HashMap<int, String> &r_funcs) {