### 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 (p_context.base == nullptr) {
		return false;
	}
	const GDScriptParser::GetNodeNode *get_node = nullptr;
	switch (p_subscript->base->type) {
		case GDScriptParser::Node::GET_NODE: {
			get_node = static_cast<GDScriptParser::GetNodeNode *>(p_subscript->base);
		} break;
		case GDScriptParser::Node::IDENTIFIER: {
			const GDScriptParser::IdentifierNode *identifier_node = static_cast<GDScriptParser::IdentifierNode *>(p_subscript->base);
			switch (identifier_node->source) {
				case GDScriptParser::IdentifierNode::Source::MEMBER_VARIABLE: {
					if (p_context.current_class != nullptr) {
						const StringName &member_name = identifier_node->name;
						const GDScriptParser::ClassNode *current_class = p_context.current_class;
						if (current_class->has_member(member_name)) {
							const GDScriptParser::ClassNode::Member &member = current_class->get_member(member_name);
							if (member.type == GDScriptParser::ClassNode::Member::VARIABLE) {
								const GDScriptParser::VariableNode *variable = static_cast<GDScriptParser::VariableNode *>(member.variable);
								if (variable->initializer && variable->initializer->type == GDScriptParser::Node::GET_NODE) {
									get_node = static_cast<GDScriptParser::GetNodeNode *>(variable->initializer);
								}
							}
						}
					}
				} break;
				case GDScriptParser::IdentifierNode::Source::LOCAL_VARIABLE: {