As for Blizzard I have no idea about the other Blizzard games, but I play Diablo 4 using Lutris, other than one update that caused the Battle.net launcher problems it works fine, at least for D4 (and D3).
Destiny 2 is another example, turning on BattlEye on Proton is literally flipping a switch in the SDK. And they had a Destiny build for Linux because it was running on Stadia. But Destiny has a horrible codebase, and even with BattlEye on Windows there is a decent chunk of hard cheating.
And its not that just the non-competitive games choose to allow Proton. Halo and Apex Legends are good examples that play on Proton.
Blizz games are definitely doable now for the most part.
I had to disable online features in Elden Ring in order to get rid of multitude of messages from other players. That was on Steam on Linux.
I haven't tried friend summoninig, but online features did work for sure.
I also enjoy playing on Linux but this really depends on the type of games you play. If you play a lot of multiplayer games, you will be disappointed on Linux, Riot games won't work, Blizzard games won't work, Fortnite won't work
Even with Elden Ring that runs perfectly on my Linux machine, I cannot use any multiplayer features (summoning friends, reading messages etc.) because the EAC anticheat doesn't work on Linux