I had the same on a UUA open jaw booking I was making the other day. Call centre staff transferred me to another dept and the new agent answered and said "I believe you're looking for flights to XYZ on the dates of XYZ". I said the dates were wrong but asked how they got this and they said they looked at my search history.
And to the OP: No, GDPR has nothing to do with this. It's not personally identifiable information and you are discussing your BA search history with BA themselves.