### 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)

vs = memnew(VSeparator);
	vs->set_custom_minimum_size(Size2(30 * EDSCALE, 0));
	hb->add_child(vs);
	pin = memnew(Button);
	pin->set_flat(true);
	pin->set_toggle_mode(true);
	hb->add_child(pin);
	tree = memnew(Tree);
	tree->set_hide_root(true);
	tree->set_columns(5);
	tree->set_column_titles_visible(true);
	tree->set_column_title(0, TTR("Properties"));
	tree->set_column_expand(0, true);
	tree->set_column_title(1, TTR("Spawn"));
	tree->set_column_expand(1, false);
	tree->set_column_custom_minimum_width(1, 100);
	tree->set_column_title(2, TTR("Sync"));
	tree->set_column_custom_minimum_width(2, 100);
	tree->set_column_title(3, TTR("Watch"));
	tree->set_column_custom_minimum_width(3, 100);
	tree->set_column_expand(2, false);
	tree->set_column_expand(3, false);
	tree->set_column_expand(4, false);
	tree->create_item();
	tree->connect("button_clicked", callable_mp(this, &ReplicationEditor::_tree_button_pressed));
	tree->connect("item_edited", callable_mp(this, &ReplicationEditor::_tree_item_edited));
	tree->set_v_size_flags(SIZE_EXPAND_FILL);
	vb->add_child(tree);
	drop_label = memnew(Label);
	drop_label->set_text(TTR("Add properties using the options above, or\ndrag them them from the inspector and drop them here."));