my personal preference would be to create a contract between the caller and the handler such that if an error occurs, a known response would be sent back such that the caller could understand what had happened.
This known object may have things that appear in exceptions, e.g. the exception message, the cause, even a stack trace perhaps, but that'd be pushing it. I'd rather have something more domain specific to what I was doing rather than something technology specific which could change in the future when I changed the underlying tech from Postgres to MariaDB for example