Digital claims for the Barbarian edition can be found in two places. The first thing you should do is use the claim form found on this page:
https://claim.conanexiles.com/
This is where you can register your t-shirt shipping information, as well as register your email address for receiving specific digital bonuses. Any bonuses not mailed to you will be found in the game’s installation folder. These can be found by right-clicking Conan Exiles in your Steam library, going to Properties -> Local Files -> Browse Local Files. They will be located in folders named after the items, such as Artbook, Soundtracks, Twitch overlay and Wallpapers.