### 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
if (_debug_parse_err_line >= 0) {
		return "";
	}
	ERR_FAIL_INDEX_V(p_level, _call_stack.stack_pos, "");
	int l = _call_stack.stack_pos - p_level - 1;
	return _call_stack.levels[l].function->get_name();
}
String GDScriptLanguage::debug_get_stack_level_source(int p_level) const {
	if (_debug_parse_err_line >= 0) {
		return _debug_parse_err_file;
	}
	ERR_FAIL_INDEX_V(p_level, _call_stack.stack_pos, "");
	int l = _call_stack.stack_pos - p_level - 1;
	return _call_stack.levels[l].function->get_source();
}
void GDScriptLanguage::debug_get_stack_level_locals(int p_level, List<String> *p_locals, List<Variant> *p_values, int p_max_subitems, int p_max_depth) {
	if (_debug_parse_err_line >= 0) {
		return;
	}
	ERR_FAIL_INDEX(p_level, _call_stack.stack_pos);
	int l = _call_stack.stack_pos - p_level - 1;
	GDScriptFunction *f = _call_stack.levels[l].function;
	List<Pair<StringName, int>> locals;
	f->debug_get_stack_member_state(*_call_stack.levels[l].line, &locals);
	for (const Pair<StringName, int> &E : locals) {
		p_locals->push_back(E.first);
		p_values->push_back(_call_stack.levels[l].stack[E.second]);
	}
}
void GDScriptLanguage::debug_get_stack_level_members(int p_level, List<String> *p_members, List<Variant> *p_values, int p_max_subitems, int p_max_depth) {