Personally I prefer having Battle.net in Lutris (or something else like Bottles) even if you can run it through Steam. I just dislike using a launcher to open another launcher and Lutris avoids that.

I can understand that the Steam method would be a little easier for some people, but using Lutris for something as popular as Battle.net is really easy too. You just click "Add" and search for "Battle.net" and it does the rest automatically, even downloading the installer. The only thing to be aware of is that you should close the launcher when it gets to the point you are asked to log in which completes the installation, but Lutris tells you that as well.

‘Works fine’ is not true yet, currently.

Especially annoying on steam deck. Is this a Linux issue? No. It absolutely is not.

how did you do it? mine does not start after installing.