Steam Deck user here. I am also getting this problem starting today. It’s really good to hear others are suddenly having this. I haven’t tried a whole lot myself yet, as I had to install the app in a sort of roundabout way in the first place so it would work on a SteamOS system.
I noticed the discussion is more active at another forum post: “BLZBNTBNA00000005 (Battle.net Agent ist zum Schlafen gegange”