### 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
ERR_FAIL_COND(p_recursion_depth > COMPLETION_RECURSION_LIMIT);
	if (!p_parent_only) {
		bool outer = false;
		const GDScriptParser::ClassNode *clss = p_class;
		int classes_processed = 0;
		while (clss) {
			for (int i = 0; i < clss->members.size(); i++) {
				const int location = p_recursion_depth == 0 ? classes_processed : (p_recursion_depth | ScriptLanguage::LOCATION_PARENT_MASK);
				const GDScriptParser::ClassNode::Member &member = clss->members[i];
				ScriptLanguage::CodeCompletionOption option;
				switch (member.type) {
					case GDScriptParser::ClassNode::Member::VARIABLE:
						if (p_only_functions || outer || (p_static && !member.variable->is_static)) {
							continue;
						}
						option = ScriptLanguage::CodeCompletionOption(member.variable->identifier->name, ScriptLanguage::CODE_COMPLETION_KIND_MEMBER, location);
						break;
					case GDScriptParser::ClassNode::Member::CONSTANT:
						if (p_only_functions) {
							continue;
						}
						if (r_result.has(member.constant->identifier->name)) {
							continue;