### 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
switch (member.type) {
					case GDScriptParser::ClassNode::Member::CLASS: {
						ScriptLanguage::CodeCompletionOption option(member.m_class->identifier->name, ScriptLanguage::CODE_COMPLETION_KIND_CLASS, ScriptLanguage::LOCATION_LOCAL);
						r_result.insert(option.display, option);
					} break;
					case GDScriptParser::ClassNode::Member::ENUM: {
						if (!p_inherit_only) {
							ScriptLanguage::CodeCompletionOption option(member.m_enum->identifier->name, ScriptLanguage::CODE_COMPLETION_KIND_ENUM, ScriptLanguage::LOCATION_LOCAL);
							r_result.insert(option.display, option);
						}
					} break;
					case GDScriptParser::ClassNode::Member::CONSTANT: {
						if (member.constant->get_datatype().is_meta_type && p_context.current_class->outer != nullptr) {
							ScriptLanguage::CodeCompletionOption option(member.constant->identifier->name, ScriptLanguage::CODE_COMPLETION_KIND_CLASS, ScriptLanguage::LOCATION_LOCAL);
							r_result.insert(option.display, option);
						}
					} break;
					default:
						break;
				}
			}
			current = current->outer;
		}
	}
	
	List<StringName> global_classes;
	ScriptServer::get_global_class_list(&global_classes);
	for (const StringName &E : global_classes) {
		ScriptLanguage::CodeCompletionOption option(E, ScriptLanguage::CODE_COMPLETION_KIND_CLASS, ScriptLanguage::LOCATION_OTHER_USER_CODE);
		r_result.insert(option.display, option);