### 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
found = true;
			} break;
			default:
				break;
		}
	}
	
	if (found && r_type.type.kind == GDScriptParser::DataType::BUILTIN && r_type.type.builtin_type == Variant::NIL) {
		found = false;
	}
	
	
	if (!found && p_expression->get_datatype().is_hard_type()) {
		r_type.type = p_expression->get_datatype();
		if (!r_type.assigned_expression) {
			r_type.assigned_expression = p_expression;
		}
		found = true;
	}
	return found;
}
static bool _guess_identifier_type(GDScriptParser::CompletionContext &p_context, const GDScriptParser::IdentifierNode *p_identifier, GDScriptCompletionIdentifier &r_type) {
	static int recursion_depth = 0;
	RecursionCheck recursion(&recursion_depth);
	if (unlikely(recursion.check())) {
		ERR_FAIL_V_MSG(false, "Reached recursion limit while trying to guess type.");
	}
	
	int last_assign_line = -1;
	const GDScriptParser::ExpressionNode *last_assigned_expression = nullptr;