Ok, found a fix for Lutris
--------- Current fix for Lutris --------
Lutris → preferences → global Options → environmental variables
AS KEY add -> WINE_SIMULATE_WRITECOPY
AS Value add -> 1
I think i have the solution for Steam Deck too, but i can’t test it by myself, so i just post my solution, and i hope it’s the solution for you :
------- Fix on Steam --------
In the options of your battlenet (the place where you choose the proton compatibility), go in the “Shortcut” tab and in the field “Launch Options” put this command → WINE_SIMULATE_WRITECOPY=1 %command%
Let us know if it’s help 
If not, i know it’s possible to install Bnet with Lutris on the steam deck (just view some tutorial on the internet).