### 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
GDScriptTokenizer tokenizer;
	tokenizer.set_source_code(p_code);
	int indent = 0;
	GDScriptTokenizer::Token current = tokenizer.scan();
	while (current.type != GDScriptTokenizer::Token::TK_EOF && current.type != GDScriptTokenizer::Token::ERROR) {
		if (current.type == GDScriptTokenizer::Token::INDENT) {
			indent++;
		} else if (current.type == GDScriptTokenizer::Token::DEDENT) {
			indent--;
		}
		if (indent == 0 && current.type == GDScriptTokenizer::Token::FUNC) {
			current = tokenizer.scan();
			if (current.is_identifier()) {
				String identifier = current.get_identifier();
				if (identifier == p_function) {
					return current.start_line;
				}
			}
		}
		current = tokenizer.scan();
	}
	return -1;
}
Script *GDScriptLanguage::create_script() const {
	return memnew(GDScript);
}
thread_local int GDScriptLanguage::_debug_parse_err_line = -1;
thread_local String GDScriptLanguage::_debug_parse_err_file;
thread_local String GDScriptLanguage::_debug_error;
bool GDScriptLanguage::debug_break_parse(const String &p_file, int p_line, const String &p_error) {