Sorry for reporting back late. I was able to get in touch with Bitbay later on that day via their live chat support and my ETH was instantly credited to my account once I reported the issue. I got a bit scared because this was my first time using them and I sent around 7 ETH, so not a very small money either. Now I see they have published a notification on their homepage regarding possible delays with ETH deposits, which is a good move, especially for first-time users.

They are not a Scam exchange and I'm happy to close this dispute.