It is always necessary to ground the shielding for it to work at reducing noise pickup.
Unfortunately some people don’t realise this so you often see very nice-looking pictures of copper-lined cavities, but with no means of them being grounded. Because it looks so neat, others then think this must be the way to do it and so do it that way themselves rather than the necessary way of either using wires to ground the copper or running the copper over the edge of control cavities so it can mate with grounded shielding on the underside of a pickguard or a grounded metal control plate.
You may not notice a big improvement in noise in single coil mode, but it’s still worth doing.