You have to enable the option of tracking expenses and items by customer as well as making expenses and items billable under the Account and Settings to be able to get the customer field when trying to add expenses to customers. I can help guide you on how.
Log in to your QuickBooks Online (QBO) account.
Go to the Gear icon.
Select Account and Settings.
From the Bills and expenses section, select Edit.
Select the following:
Show Items table on expense and purchase forms
Track expenses and items by customer
Make expenses and items billable
(Optional) Set up the following:
Billable expense tracking
Sales tax charge
Bill payment terms
Select Save, then Done.
Once completed, you'll now be able to select a customer when entering expenses, ensure to put a check-mark in the box under the Billable column to make the expense billable to your customer.