The game displaying simply as “Hogwarts Legacy” in my Steam library despite having the Deluxe Edition

The game will always show as Hogwarts Legacy, without denoting the edition, in your Steam Library. If you have the Deluxe Edition, you can verify it in your Steam Licences page. To access such, click on your account name in the top-right corner and select Account Details from the drop-down list. On the next page, select the option View licenses and product key activations. The license name for your Hogwarts Legacy will show whether you own the Deluxe Edition.