Originally Posted by Max Lemesh
Managed to resolve it and the issue definitely was connected to my Larian account.
Once I disconnected it from GOG and PS it worked fine, if connected back it still crashed. I deleted my Larian account and made it again with the same email. Everything worked fine now, but didn’t want to sync saves. So, I deleted it again, made an account with different email, reconnected GOG and PS and voilà - everything works and syncs.

Sad it doesn't just say "hey bad email, do another one" instead of crashing on loading

Thanks, Max.
Your solution worked perfectly. It stinks having to delete one account to recreate another one with a different email address to get it working again. For me, BG III started the insta-crashing after hot fix #7.