### 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
r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS;
								r_result.class_name = obj->get_class();
							}
							
							if (r_result.class_name.begins_with("_")) {
								r_result.class_name = r_result.class_name.substr(1);
							}
							return OK;
						}
					} else {
						/*
						// Because get_integer_constant_enum and get_integer_constant don't work on @GlobalScope
						// We cannot determine the exact nature of the identifier here
						// Otherwise these codes would work
						StringName enumName = ClassDB::get_integer_constant_enum("@GlobalScope", p_symbol, true);
						if (enumName != nullptr) {
							r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS_ENUM;
							r_result.class_name = "@GlobalScope";
							r_result.class_member = enumName;
							return OK;
						}
						else {
							r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS_CONSTANT;
							r_result.class_name = "@GlobalScope";
							r_result.class_member = p_symbol;
							return OK;
						}*/
						r_result.type = ScriptLanguage::LOOKUP_RESULT_CLASS_TBD_GLOBALSCOPE;
						r_result.class_name = "@GlobalScope";
						r_result.class_member = p_symbol;