dnd 5e – If a character with the Alert feat gets a critical failure in his Perception check, are you surprised?

Because the feat of alert (PHB, page 165) says:

You can not be surprised while you are conscious.

A character with the alert feat can not be surprised while he is conscious.

"Surprised" has a clear mechanical meaning.

If a character is surprised, he can not act on his first combat turn, and after his first turn, he is no longer surprised.

A character with the Alert feat that performs a low perception control may not be ready, but never surprise him. They may not have enough time to wake up all their allies before the battle begins or they do not have time to get in position or take the necessary measures to put on a shield (before the fight). But they can never be "surprised".

Rules as written, critical failures are only for attack rolls.

It is a common rule of the house that throwing a 1 in a d20 results in a critical failure, whatever the context, but there is no rule in D & D 5e that indicates that this is the case for anything else that is not thrown away of attack, where the result is simply "you". to lose".
Note: The optional rule on page 242 of the DMG ("Critical Success or Failure") does not explicitly state that a 1 in a skill test overrides the characteristics of a feat.