### 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
Pair<String, Variant> pi;
	pi.first = "PI";
	pi.second = Math_PI;
	p_constants->push_back(pi);
	Pair<String, Variant> tau;
	tau.first = "TAU";
	tau.second = Math_TAU;
	p_constants->push_back(tau);
	Pair<String, Variant> infinity;
	infinity.first = "INF";
	infinity.second = INFINITY;
	p_constants->push_back(infinity);
	Pair<String, Variant> nan;
	nan.first = "NAN";
	nan.second = NAN;
	p_constants->push_back(nan);
}
void GDScriptLanguage::get_public_annotations(List<MethodInfo> *p_annotations) const {
	GDScriptParser parser;
	List<MethodInfo> annotations;
	parser.get_annotation_list(&annotations);
	for (const MethodInfo &E : annotations) {
		p_annotations->push_back(E);
	}
}
String GDScriptLanguage::make_function(const String &p_class, const String &p_name, const PackedStringArray &p_args) const {