### 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
w.end_line = warn.end_line;
			w.leftmost_column = warn.leftmost_column;
			w.rightmost_column = warn.rightmost_column;
			w.code = (int)warn.code;
			w.string_code = GDScriptWarning::get_name_from_code(warn.code);
			w.message = warn.get_message();
			r_warnings->push_back(w);
		}
	}
#endif
	if (err) {
		if (r_errors) {
			for (const GDScriptParser::ParserError &pe : parser.get_errors()) {
				ScriptLanguage::ScriptError e;
				e.path = p_path;
				e.line = pe.line;
				e.column = pe.column;
				e.message = pe.message;
				r_errors->push_back(e);
			}
			for (KeyValue<String, Ref<GDScriptParserRef>> E : analyzer.get_depended_parsers()) {
				GDScriptParser *depended_parser = E.value->get_parser();
				for (const GDScriptParser::ParserError &pe : depended_parser->get_errors()) {
					ScriptLanguage::ScriptError e;
					e.path = E.key;
					e.line = pe.line;
					e.column = pe.column;
					e.message = pe.message;
					r_errors->push_back(e);
				}