### 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
} else {
			arghint += par->identifier->name.operator String() + ": " + par->get_datatype().to_string();
		}
		if (par->initializer) {
			String def_val = "<unknown>";
			switch (par->initializer->type) {
				case GDScriptParser::Node::LITERAL: {
					const GDScriptParser::LiteralNode *literal = static_cast<const GDScriptParser::LiteralNode *>(par->initializer);
					def_val = literal->value.get_construct_string();
				} break;
				case GDScriptParser::Node::IDENTIFIER: {
					const GDScriptParser::IdentifierNode *id = static_cast<const GDScriptParser::IdentifierNode *>(par->initializer);
					def_val = id->name.operator String();
				} break;
				case GDScriptParser::Node::CALL: {
					const GDScriptParser::CallNode *call = static_cast<const GDScriptParser::CallNode *>(par->initializer);
					if (call->is_constant && call->reduced) {
						def_val = call->function_name.operator String() + call->reduced_value.operator String();
					}
				} break;
				case GDScriptParser::Node::ARRAY: {
					const GDScriptParser::ArrayNode *arr = static_cast<const GDScriptParser::ArrayNode *>(par->initializer);
					if (arr->is_constant && arr->reduced) {
						def_val = arr->reduced_value.operator String();
					}
				} break;
				case GDScriptParser::Node::DICTIONARY: {
					const GDScriptParser::DictionaryNode *dict = static_cast<const GDScriptParser::DictionaryNode *>(par->initializer);
					if (dict->is_constant && dict->reduced) {
						def_val = dict->reduced_value.operator String();