USO: Discounts and Promotions does not require a manual code install. However, you do need to enable a Shopify app embed in your theme in order for the app to work. App embeds allow apps like USO to perform actions on your storefront like showing a popup or giving a customer a discount.
When you first install USO and go to create your first offer, a banner at the top of the page will prompt you to enable your app embed. When you click the button in the banner, you'll be taken to your theme editor and your app embed will be enabled. You can now finish setting up offers and testing them on your storefront.
When you publish a new theme, you'll need to enable the app embed again in that new theme in order for USO to work. In your admin, click Customize next to your new theme to enter the theme editor, and click App embeds in the left-hand sidebar underneath Theme settings. Click the toggle next to USO to enable the app embed.