To get Quickbooks to auto-fill email addresses from your contact list, you'll need to log in to QuickBooks mobile app. From there, you can manually add a customer and supplier information. Please note that you need to have an email address associated with the customer/supplier already in your contact list.
Here's how from the Customers section:
Log in to your account using the QuickBooks app.
Click the Menu ☰. Then, choose Customers.
Click the Plus button to add a new customer.
Type the name of the customer that already in your contact list. Then, the email address automatically appears.