### 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 (EngineDebugger::is_active() && Thread::get_caller_id() == Thread::get_main_id()) {
		_debug_parse_err_line = p_line;
		_debug_parse_err_file = p_file;
		_debug_error = p_error;
		EngineDebugger::get_script_debugger()->debug(this, false, true);
		
		_debug_parse_err_file = String();
		_debug_error = String();
		return true;
	} else {
		return false;
	}
}
bool GDScriptLanguage::debug_break(const String &p_error, bool p_allow_continue) {
	if (EngineDebugger::is_active()) {
		_debug_parse_err_line = -1;
		_debug_parse_err_file = "";
		_debug_error = p_error;
		bool is_error_breakpoint = p_error != "Breakpoint";
		EngineDebugger::get_script_debugger()->debug(this, p_allow_continue, is_error_breakpoint);
		
		_debug_parse_err_file = String();
		_debug_error = String();
		return true;
	} else {
		return false;
	}
}
String GDScriptLanguage::debug_get_error() const {