For hots: install lutris through the nobara app store. Start it and leave it for a few minutes while you run other updates or something ( only the very first time ).

Go to the settings/preferences, ( three dots top right ), click runners, scroll all the way down to wine.

Click the cog and change the runtime from wine-.... to proton-GE. Thrn you can just install the battle.net app through lutris. From the battle.net app you can install hots.

Using the built in wine-.... Runtime I got errors like missing Microsoft arial or unable to validate certificate.

with proton it just instantly worked.

You can also add the battle.net installer as an external steam app and run/install it that way. The only downside would be that you can't play a steam game AND have bnet running ( which you can through lutris ).

Exiting battle.net doesn't seem to be enough to stop lutris running it. So you might have to click the stop button in lutris if you want to restart it.

Battle.net is a bit wonky. But once you've got it IP and running it's okay.