### 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)

List<ReplicationProperty>::Element *E = properties.find(p_path);
	ERR_FAIL_COND(!E);
	if (E->get().watch == p_enabled) {
		return;
	}
	E->get().watch = p_enabled;
	watch_props.clear();
	for (const ReplicationProperty &prop : properties) {
		if (prop.watch) {
			watch_props.push_back(p_path);
		}
	}
}
void SceneReplicationConfig::_bind_methods() {
	ClassDB::bind_method(D_METHOD("get_properties"), &SceneReplicationConfig::get_properties);
	ClassDB::bind_method(D_METHOD("add_property", "path", "index"), &SceneReplicationConfig::add_property, DEFVAL(-1));
	ClassDB::bind_method(D_METHOD("has_property", "path"), &SceneReplicationConfig::has_property);
	ClassDB::bind_method(D_METHOD("remove_property", "path"), &SceneReplicationConfig::remove_property);
	ClassDB::bind_method(D_METHOD("property_get_index", "path"), &SceneReplicationConfig::property_get_index);
	ClassDB::bind_method(D_METHOD("property_get_spawn", "path"), &SceneReplicationConfig::property_get_spawn);
	ClassDB::bind_method(D_METHOD("property_set_spawn", "path", "enabled"), &SceneReplicationConfig::property_set_spawn);
	ClassDB::bind_method(D_METHOD("property_get_sync", "path"), &SceneReplicationConfig::property_get_sync);
	ClassDB::bind_method(D_METHOD("property_set_sync", "path", "enabled"), &SceneReplicationConfig::property_set_sync);
	ClassDB::bind_method(D_METHOD("property_get_watch", "path"), &SceneReplicationConfig::property_get_watch);
	ClassDB::bind_method(D_METHOD("property_set_watch", "path", "enabled"), &SceneReplicationConfig::property_set_watch);
}