### 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
p_delimiters->push_back("#");
}
void GDScriptLanguage::get_doc_comment_delimiters(List<String> *p_delimiters) const {
	p_delimiters->push_back("##");
}
void GDScriptLanguage::get_string_delimiters(List<String> *p_delimiters) const {
	p_delimiters->push_back("\" \"");
	p_delimiters->push_back("' '");
	p_delimiters->push_back("\"\"\" \"\"\"");
	p_delimiters->push_back("''' '''");
	
}
bool GDScriptLanguage::is_using_templates() {
	return true;
}
Ref<Script> GDScriptLanguage::make_template(const String &p_template, const String &p_class_name, const String &p_base_class_name) const {
	Ref<GDScript> scr;
	scr.instantiate();
	String processed_template = p_template;
	bool type_hints = false;
#ifdef TOOLS_ENABLED
	type_hints = EDITOR_GET("text_editor/completion/add_type_hints");
#endif
	if (!type_hints) {
		processed_template = processed_template.replace(": int", "")
									 .replace(": Shader.Mode", "")
									 .replace(": VisualShader.Type", "")
									 .replace(": float", "")
									 .replace(": String", "")