### Godot version

4.1.dev4

### System information

Windows 10 Godot 4.1.dev4

### Issue description

The watched property in the Multiplayer Synchronizer node is supposed to pass the variable through the network only when it changes, but as I use the network profiler, it is evidently not working as intended

### Steps to reproduce

Open 2 debug instances on the project I will give, use the network profiler and you will see the variable does not change, although it goes up to 780b/s on the network

### Minimal reproduction project

[minimalproject.zip](https://github.com/godotengine/godot/files/11659414/minimalproject.zip)

if (!current) {
		error_dialog->set_text(TTR("Please select a MultiplayerSynchronizer first."));
		error_dialog->popup_centered();
		return;
	}
	if (current->get_root_path().is_empty()) {
		error_dialog->set_text(TTR("The MultiplayerSynchronizer needs a root path."));
		error_dialog->popup_centered();
		return;
	}
	String np_text = np_line_edit->get_text();
	if (np_text.is_empty()) {
		error_dialog->set_text(TTR("Property/path must not be empty."));
		error_dialog->popup_centered();
		return;
	}
	int idx = np_text.find(":");
	if (idx == -1) {
		np_text = ".:" + np_text;
	} else if (idx == 0) {
		np_text = "." + np_text;
	}
	NodePath path = NodePath(np_text);
	_add_sync_property(path);
}
void ReplicationEditor::_np_text_submitted(const String &p_newtext) {