### 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 ("Variant" == p_symbol) {
		r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS;
		r_result.class_name = "Variant";
		return OK;
	}
	if ("PI" == p_symbol || "TAU" == p_symbol || "INF" == p_symbol || "NAN" == p_symbol) {
		r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS_CONSTANT;
		r_result.class_name = "@GDScript";
		r_result.class_member = p_symbol;
		return OK;
	}
	GDScriptParser parser;
	parser.parse(p_code, p_path, true);
	GDScriptParser::CompletionContext context = parser.get_completion_context();
	context.base = p_owner;
	
	if (context.type != GDScriptParser::COMPLETION_ATTRIBUTE) {
		
		
		if (GDScriptUtilityFunctions::function_exists(p_symbol) || "assert" == p_symbol || "preload" == p_symbol) {
			r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS_METHOD;
			r_result.class_name = "@GDScript";
			r_result.class_member = p_symbol;
			return OK;
		}
	}
	GDScriptAnalyzer analyzer(&parser);
	analyzer.analyze();
	if (context.current_class && context.current_class->extends.size() > 0) {
		bool success = false;