Earlier today, I was spreading a temporary fix that involved rolling back Battle.net to 14494. Courtesy of Doogie (M.D.) on the Lutris Discord server, the answer to allowing proper updates to 14542 is simply an environment variable WINE_SIMULATE_WRITECOPY=1:

Mini tutorial based on your method of installation:

Lutris System options

Steam launch options: WINE_SIMULATE_WRITECOPY=1 %command%

Do this for every shortcut for every game you have installed via Battle.net