How do I email preorder customers about a delay or new ship date? (Essent Preorder Back in Stock app)

Use the Preorder update email. It's always sent manually, when you choose.

Set up the template once: Preorder → Settings → Notifications → Preorder update email → Customize.
Go to Preorder → Preorders, filter or search for the orders, and tick them (or leave them unticked to send to the whole filtered list).
Choose Send update for N selected, edit the subject and text for this send if needed, and click Send.

Use {orderName} to show the order number. The update email can't be translated or scheduled for a date.