### 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 (!script.ends_with(".gd")) {
															
															
															script = script.get_basename() + ".gd";
														}
														if (FileAccess::exists(script)) {
															Error err = OK;
															Ref<GDScriptParserRef> parser = GDScriptCache::get_parser(script, GDScriptParserRef::INTERFACE_SOLVED, err);
															if (err == OK) {
																r_type.type.type_source = GDScriptParser::DataType::ANNOTATED_EXPLICIT;
																r_type.type.script_path = script;
																r_type.type.class_type = parser->get_parser()->get_tree();
																r_type.type.is_constant = false;
																r_type.type.kind = GDScriptParser::DataType::CLASS;
																r_type.value = Variant();
																p_context.dependent_parsers.push_back(parser);
																found = true;
															}
														}
														break;
													}
												}
											}
										}
									}
								}
								if (!found && all_is_const && baseptr) {
									Vector<const Variant *> argptr;
									for (int i = 0; i < args.size(); i++) {
										argptr.push_back(&args[i]);