You are misunderstanding the issue. It's not asking
before the update (as most programs that prompt you to update do).
By the time that dialog box is displayed, the application has already replaced itself on disk (with code chosen arbitrarily by the bitwarden developers, or anyone in possession of their credentials), and the new code will be executed automatically without user intervention the next time the app is launched, which happens automatically if the computer is rebooted (like if there is a momentary power failure, or you hit "okay" on an OS update, or your battery dies and later you plug it back in to power).
This grants the developers (as well as anyone who can compromise their credentials) unlimited remote access to your entire password vault the next time you unlock it.