### Godot version

v4.2.rc.mono.custom_build [ad72de508]

### System information

Windows 10

### Issue description

As I pointed out several times earlier in [#80284](https://github.com/godotengine/godot/pull/80284#issuecomment-1722120503), the references to singletons in `GDScript` are still not updated after the `GDExtension` reload.

https://github.com/godotengine/godot/assets/7782218/f90052a5-0de2-4310-8235-f0b9e2f74b3a

Singletons themselves are updated and work correctly, but references to these singletons are not updated in `@tool` scripts. That is, `Engine.get_singleton` returns the actual working reference, but using the singleton directly through its name causes errors.

### Steps to reproduce

* Clone `4.2.reload_singleton` branch from the MRP repository https://github.com/DmitriySalnikov/gde_test_cases/tree/4.2.reload_singleton
* Build as usual
* Open the project from the `project/` folder
* Add one character to the source code and rebuild
* Focus on the editor to reload extension
* Watch for error spam when calling by singleton name

### Minimal reproduction project

https://github.com/DmitriySalnikov/gde_test_cases/tree/4.2.reload_singleton
const GDScriptParser::ClassNode *c = parser.get_tree();
			if (base_cache.is_valid()) {
				base_cache->inheriters_cache.erase(get_instance_id());
				base_cache = Ref<GDScript>();
			}
			GDScriptParser::DataType base_type = parser.get_tree()->base_type;
			if (base_type.kind == GDScriptParser::DataType::CLASS) {
				Ref<GDScript> bf = GDScriptCache::get_full_script(base_type.script_path, err, path);
				if (err == OK) {
					bf = Ref<GDScript>(bf->find_class(base_type.class_type->fqcn));
					if (bf.is_valid()) {
						base_cache = bf;
						bf->inheriters_cache.insert(get_instance_id());
					}
				}
			}
			members_cache.clear();
			member_default_values_cache.clear();
			_signals.clear();
			members_cache.push_back(get_class_category());
			for (int i = 0; i < c->members.size(); i++) {
				const GDScriptParser::ClassNode::Member &member = c->members[i];
				switch (member.type) {
					case GDScriptParser::ClassNode::Member::VARIABLE: {
						if (!member.variable->exported) {
							continue;
						}
						members_cache.push_back(member.variable->export_info);
						Variant default_value = analyzer.make_variable_default_value(member.variable);
						member_default_values_cache[member.variable->identifier->name] = default_value;