### 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)

properties.erase(p_path);
	sync_props.erase(p_path);
	spawn_props.erase(p_path);
	watch_props.clear();
}
bool SceneReplicationConfig::has_property(const NodePath &p_path) const {
	for (int i = 0; i < properties.size(); i++) {
		if (properties[i].name == p_path) {
			return true;
		}
	}
	return false;
}
int SceneReplicationConfig::property_get_index(const NodePath &p_path) const {