### 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 (prop.sync) {
				sync_props.push_back(prop.name);
			} else {
				sync_props.erase(prop.name);
			}
			return true;
		} else if (what == "spawn") {
			if ((bool)p_value == prop.spawn) {
				return true;
			}
			prop.spawn = p_value;
			if (prop.spawn) {
				spawn_props.push_back(prop.name);
			} else {
				spawn_props.erase(prop.name);
			}
			return true;
		} else if (what == "watch") {
			prop.watch = p_value;
			if (prop.watch) {
				watch_props.push_back(prop.name);
			} else {
				watch_props.erase(prop.name);
			}
			return true;
		}
	}
	return false;
}
bool SceneReplicationConfig::_get(const StringName &p_name, Variant &r_ret) const {