Apparently there was a pre-release update for Overwatch.
When it finished, I got the BLZBNTAGT00000BB8 error.
I have the exact same problem on 3 different computers. I tried everything from the support page
After trying to repair the game, not it says that an update is available for the current version of Overwatch, after trying to update it, I get the same error. So now, I’m unable to play the game because it requires an update.