### 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
}
					r_arghint = _make_arguments_hint(info, p_argidx);
				}
				if (p_argidx == 0 && ClassDB::is_parent_class(class_name, SNAME("Node")) && (p_method == SNAME("get_node") || p_method == SNAME("has_node"))) {
					
					List<PropertyInfo> props;
					ProjectSettings::get_singleton()->get_property_list(&props);
					for (const PropertyInfo &E : props) {
						String s = E.name;
						if (!s.begins_with("autoload/")) {
							continue;
						}
						String name = s.get_slice("/", 1);
						ScriptLanguage::CodeCompletionOption option("/root/" + name, ScriptLanguage::CODE_COMPLETION_KIND_NODE_PATH);
						option.insert_text = option.display.quote(quote_style);
						r_result.insert(option.display, option);
					}
				}
				if (p_argidx == 0 && method_args > 0 && ClassDB::is_parent_class(class_name, SNAME("InputEvent")) && p_method.operator String().contains("action")) {
					
					List<PropertyInfo> props;
					ProjectSettings::get_singleton()->get_property_list(&props);
					for (const PropertyInfo &E : props) {
						String s = E.name;
						if (!s.begins_with("input/")) {
							continue;
						}
						String name = s.get_slice("/", 1);
						ScriptLanguage::CodeCompletionOption option(name, ScriptLanguage::CODE_COMPLETION_KIND_CONSTANT);
						option.insert_text = option.display.quote(quote_style);