Do my Member Surfs need to be surfed by the expiry date, or just booked by then?

No. Your Member Surfs do not need to be surfed by the expiry date.

They do need to be booked by the expiry date, but the surf session itself can take place after that date, including into the following month.

The exact booking expiry date is shown under My Membership & Multipacks in your Membership Dashboard.