From what I understand you have to re-purchase if you already own it on Battle.net, which is pretty frustrating. As playing on the Steam Deck would be much easier in Steam.
I have done this, but it is clunky having to first launch the Battle.net launcher, then launch Diablo IV on the steam deck. It would be much better to skip the launcher. I would hope when you bought the game through steam you wouldn’t be forced to go through the launcher.