Voting against this, as I consider the "at all" message a bug and that it should be identical to the message of non-trapped doors. Why should you be able to determine a trap status of a door based on an in-game message format?

Well, trapped doors are even more unbudging than the normal doors.

So how do you try harder -- quaff a potion of Boost Strength?

Unfortunately, I'm against it too. The message is supposed to reflect the PC's thoughts, and if they don't know of the trap, there's no reason they would think differently at trapped and non-trapped doors. The game should not just hand out information that the player isn't supposed to have access to.

Except perhaps if the "at all" part, which corresponds to being trapped indicates that the door seems absolutely impenetrable, and your character gives up on kicking it down. But
1. The door being in impenetrable is in fact untrue;
2. There's no good reason a trap would in and of itself make a door more stable (and I also don't think the chances of kicking it down are actually any different in-game). Actually, if a trap is supposed to injure someone, you wouldn't want to make it impossible to activate; unless you just want to prevent them from entering, and trap is just an additional layer of protection.

So all in all, I agree with Harkila that the "at all" differentiation should be removed too, or made less reliable (though if I'm being honest I'm not entirely sure how the format of these messages behave at this exact time either, not paying much attention to them usually, and generally avoiding kicking down doors if at all possible).

Message "Try again - and harder!" looks out of place to me since it was introduced. I would change it on normal doors with "The door cracks!", "The door shakes!", "The door starts to break!". This way for doors that doesn't budge at all having no this message would make more sense.