To wish list items in Scarlet Nexus, you must first unlock the item exchange. The item exchange is a unique feature that involves Satori the Archivist's shop, and will allow you to exchange materials you get in the field for items.
That said, to unlock the exchange in Scarlet Nexus, you first need to get past the first standby stage and reach Phase two. After this point, you will be able to access the item exchange via an option in Satori the Archivist's store.
Once the exchange is unlocked, you will be able to wish list items by pressing down whatever button shows up for you on the bottom left of your screen. For example, on an Xbox controller, RS is the analog stick, but this will be different between platforms. So check the key listing and hit that button to wish list any item you hover over from the listings.
Also, when you wish list an item in Scarlet Nexus, the game will let you know when you have enough materials to exchange for the item. The game will do this in the form of a notification on the left of your screen, and you can also check the status of items via the tab in the library called wish list.
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