Is the remaining balance on a partial payment charged automatically? (Essent Preorder Back in Stock app)

No. The due date only tells the customer when payment is expected. You collect the balance, whenever you're ready, before or after that date.

Collect the balance

• In bulk: Preorder → Preorders tab → Partially paid → select orders → Collect payments. You can tick the option to send a Shopify invoice if a card fails. Needs the Lite plan or higher.
• One order: open the order in Shopify → Collect payment.
• Automatically: use the Shopify Flow action Collect preorder balance now, for example on a date or when stock arrives.

Never use Shopify's bulk "Capture payments" in the order list. It marks orders as paid without charging and removes what's needed to collect the balance.

Good to know

• Partial payments need Shopify Payments.
• There are two payments only: the deposit (can be 0) and one balance. Three or more instalments aren't supported.
• The due date can't be removed because Shopify requires a payment schedule. You can remove the date from your preorder message and write, for example, "Balance charged when we ship".
• The app sends no balance reminders. Use Shopify Flow if you want them.

Full guides: Collect remaining balances and Managing partial payments.