### 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
last_assign_line = local.constant->initializer->end_line;
					last_assigned_expression = local.constant->initializer;
				}
				break;
			case GDScriptParser::SuiteNode::Local::PARAMETER:
				if (local.parameter->initializer) {
					last_assign_line = local.parameter->initializer->end_line;
					last_assigned_expression = local.parameter->initializer;
				}
				is_function_parameter = true;
				break;
			default:
				break;
		}
	}
	while (suite) {
		for (int i = 0; i < suite->statements.size(); i++) {
			if (suite->statements[i]->end_line >= p_context.current_line) {
				break;
			}
			switch (suite->statements[i]->type) {
				case GDScriptParser::Node::ASSIGNMENT: {
					const GDScriptParser::AssignmentNode *assign = static_cast<const GDScriptParser::AssignmentNode *>(suite->statements[i]);
					if (assign->end_line > last_assign_line && assign->assignee && assign->assigned_value && assign->assignee->type == GDScriptParser::Node::IDENTIFIER) {
						const GDScriptParser::IdentifierNode *id = static_cast<const GDScriptParser::IdentifierNode *>(assign->assignee);
						if (id->name == p_identifier->name && id->source == p_identifier->source) {
							last_assign_line = assign->assigned_value->end_line;
							last_assigned_expression = assign->assigned_value;
						}
					}