MacBook Pro M1, Ventura 13.5 here and same issue 
Same here. M1 Ventura Version 13.4.1 (22F82).
I’m uncertain if this helps to narrow down the issue, but before the crashes occurred, a friend invited me to a party of four and none of us had a “ready” button (we wanted to queue for ranked).
Instead, we joined a lobby chat. We disbanded the group and I still had no button and couldn’t select any game mode. So, I decided to restart the game and it’s crashing ever since.
ETA: I tried to install it via Parallels, and it wouldn’t start either.
Seems like US forums have more vibe, see https://us.forums.blizzard.com/en/heroes/t/mac-game-crashes-on-startup/60358
I’d probably recommend you subscribe to that one, since EU doesn’t get much love
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customer support replied on u.s one so should be fixed soon hopefully
off topic here, my mic doesnt work in voice chat either, recently owner of same model, do u have the same problem? , any advice would be appreciated, or a link to something usefull…tks
US support answered with this:
Hello again everyone,
Thank you all for the reports and error codes that have been shared. We have passed along the info to our engineers and they are investigating the source of these crashes affecting all MacOS versions.
At the moment we do not have a work around to prevent the crash, but once we have have more info to share we will provide an update in this thread.
Good news, it’s fixed