The customer logout button can be displayed depending on the Header layout chosen within your theme customizer.
In Superstore, the customer account logout link is available for Traditional and Minimal Header layouts, while the Basic layout only displays this in mobile view.
Traditional
The logout will appear on the right side of the Header, beside the customer's name.
Minimal
Clicking the ( ☰ ) menu button will expand the Navigation and show the logout link on the right side of MY ACCOUNT.
Basic
The logout link will only appear in mobile view. When clicking the ( ☰ ) menu button, you can find the option on top of the menu slider, beside MY ACCOUNT.
Adding this in desktop view will involve code customization and you can reach out to Shopify Experts for assistance.