### 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
_find_built_in_variants(r_result, true);
	List<StringName> native_types;
	ClassDB::get_class_list(&native_types);
	for (const StringName &E : native_types) {
		if (ClassDB::is_class_exposed(E) && !Engine::get_singleton()->has_singleton(E)) {
			ScriptLanguage::CodeCompletionOption option(E, ScriptLanguage::CODE_COMPLETION_KIND_CLASS);
			r_result.insert(option.display, option);
		}
	}
	if (p_context.current_class) {
		if (!p_inherit_only && p_context.current_class->base_type.is_set()) {
			
			List<StringName> enums;
			ClassDB::get_enum_list(p_context.current_class->base_type.native_type, &enums);
			for (const StringName &E : enums) {
				ScriptLanguage::CodeCompletionOption option(E, ScriptLanguage::CODE_COMPLETION_KIND_ENUM);
				r_result.insert(option.display, option);
			}
		}
		
		const GDScriptParser::ClassNode *current = p_context.current_class;
		while (current) {
			for (int i = 0; i < current->members.size(); i++) {
				const GDScriptParser::ClassNode::Member &member = current->members[i];