I got the new update this morning, and the color customization button that the notes mentioned appears and functions in the medbay, but the new DLC enemies aren't present in any of the areas they were added to, and in the US PS4 store there's no new DLC available for download. Going to the PS4 store for other regions shows the Cutting Edge DLC available, in fact the Australian PS4 store is the first result on google for "The Surge Cutting Edge." It also seems to be available on the Microsoft store in the US, but not on the Playstation store.
Thank you very much for the reply! I was worried I was just missing some very obvious way to unlock it! I started a new character to check it out when I saw the update this morning, then I ended up playing through a huge chunk of the game, getting into a new character build, before I even realized I'd totally forgotten to look for the new content. Any excuse to play through this game again is a good one, thank you for letting me know when to look for the DLC!