This was one of the easiest ways I found to do it (thanks to an old reddit steamdeck subreddit post before the recent chaos) https://github.com/moraroy/NonSteamLaunchers-On-Steam-Deck
A few instructions and it does basically everything for battle net, gog, epic, etc. For battle.net I did seem to have to install D4 in desktop and then it loads straight up on it’s added battle.net launcher in game mode.
I use DDG and fall back to Google if that flat out isn’t working.