Responses
I think he thought he knew the password since it was supposed to be En's birthday. He only found out later on that the "birthday" En meant was the date he decided to live as an omega which was the day Habaki got hospitalized
He knew from the start the day alpha got hospitalized he read it that's why he mentioned "you did great work at hiding I still believed in your words that's More En like"
!! Spoilers !!
Habaki said that he knew the password for En's laptop in ch 2. So shouldn't he already know that En is a beta? That's long before the kidnapping