### 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
ScriptLanguage::CodeCompletionOption set("set", ScriptLanguage::CODE_COMPLETION_KIND_PLAIN_TEXT);
			options.insert(set.display, set);
			r_forced = true;
		} break;
		case GDScriptParser::COMPLETION_PROPERTY_METHOD: {
			if (!completion_context.current_class) {
				break;
			}
			for (int i = 0; i < completion_context.current_class->members.size(); i++) {
				const GDScriptParser::ClassNode::Member &member = completion_context.current_class->members[i];
				if (member.type != GDScriptParser::ClassNode::Member::FUNCTION) {
					continue;
				}
				if (member.function->is_static) {
					continue;
				}
				ScriptLanguage::CodeCompletionOption option(member.function->identifier->name, ScriptLanguage::CODE_COMPLETION_KIND_FUNCTION);
				options.insert(option.display, option);
			}
			r_forced = true;
		} break;
		case GDScriptParser::COMPLETION_ASSIGN: {
			GDScriptCompletionIdentifier type;
			if (!completion_context.node || completion_context.node->type != GDScriptParser::Node::ASSIGNMENT) {
				break;
			}
			if (!_guess_expression_type(completion_context, static_cast<const GDScriptParser::AssignmentNode *>(completion_context.node)->assignee, type)) {
				_find_identifiers(completion_context, false, options, 0);
				r_forced = true;
				break;