### 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
const String quote_style = EDITOR_GET("text_editor/completion/use_single_quotes") ? "'" : "\"";
	GDScriptParser parser;
	GDScriptAnalyzer analyzer(&parser);
	parser.parse(p_code, p_path, true);
	analyzer.analyze();
	r_forced = false;
	HashMap<String, ScriptLanguage::CodeCompletionOption> options;
	GDScriptParser::CompletionContext completion_context = parser.get_completion_context();
	completion_context.base = p_owner;
	bool is_function = false;
	switch (completion_context.type) {
		case GDScriptParser::COMPLETION_NONE:
			break;
		case GDScriptParser::COMPLETION_ANNOTATION: {
			List<MethodInfo> annotations;
			parser.get_annotation_list(&annotations);
			for (const MethodInfo &E : annotations) {
				ScriptLanguage::CodeCompletionOption option(E.name.substr(1), ScriptLanguage::CODE_COMPLETION_KIND_PLAIN_TEXT);
				if (E.arguments.size() > 0) {
					option.insert_text += "(";
				}
				options.insert(option.display, option);
			}
			r_forced = true;
		} break;
		case GDScriptParser::COMPLETION_ANNOTATION_ARGUMENTS: {
			if (completion_context.node == nullptr || completion_context.node->type != GDScriptParser::Node::ANNOTATION) {
				break;
			}