If you have an Amex card and didnt get another email today then you're probably safe. BA got given a grace period by them when the big one happened, this time around BA didn't move quick enough and Amex issued an email ahead of them and basically called them out. When I got the highly detailed "hey we've got your back" email from Amex the other week I knew I was about to be told by BA my details had been compromised more/ a 2nd time. They even missed their own deadline of 12:00 the day after Amex issued their reassurance email and I only got BA's email the Tuesday afterwards.

Fingers crossed for you getting some birthday miles though and HAPPY BIRTHDAY for 2moro.