Basically sleep well and soundly. A cute goodnight message

Anatidaephobia is defined as a pervasive, irrational fear that one is being watched by a duck. The anatidaephobic individual fears that no matter where they are or what they are doing, a duck watches.

Anatidaephobia is derived from the Greek word "anatidae", meaning ducks, geese or swans and "phobos" meaning fear.

Meaning Sleep well.
Very well used phrase in the English - speaking world. It's been common at bedtime for many years in the form of "good night, sleep tight, don't let the bedbugs bite", or something like that.