### 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
GDScriptParser::DataType id_type;
	GDScriptParser::SuiteNode *suite = p_context.current_suite;
	bool is_function_parameter = false;
	bool can_be_local = true;
	switch (p_identifier->source) {
		case GDScriptParser::IdentifierNode::MEMBER_VARIABLE:
		case GDScriptParser::IdentifierNode::MEMBER_CONSTANT:
		case GDScriptParser::IdentifierNode::MEMBER_FUNCTION:
		case GDScriptParser::IdentifierNode::MEMBER_SIGNAL:
		case GDScriptParser::IdentifierNode::MEMBER_CLASS:
		case GDScriptParser::IdentifierNode::INHERITED_VARIABLE:
		case GDScriptParser::IdentifierNode::STATIC_VARIABLE:
			can_be_local = false;
			break;
		default:
			break;
	}
	if (can_be_local && suite && suite->has_local(p_identifier->name)) {
		const GDScriptParser::SuiteNode::Local &local = suite->get_local(p_identifier->name);
		id_type = local.get_datatype();
		
		switch (local.type) {
			case GDScriptParser::SuiteNode::Local::VARIABLE:
				if (local.variable->initializer) {
					last_assign_line = local.variable->initializer->end_line;
					last_assigned_expression = local.variable->initializer;
				}
				break;
			case GDScriptParser::SuiteNode::Local::CONSTANT:
				if (local.constant->initializer) {