A date picker can only be opened by clicking it with a mouse. Keyboard users can't reach it at all. Which POUR principle does this break first?

Operable means every user can work every control. WCAG 2.1.1 Keyboard, a level A rule, sits under this principle, and a mouse-only control breaks it.

"Perceivable" is the tempting wrong answer. The user can see the date picker fine. The problem is that they can't use it. "Robust" is about working with assistive technology through correct roles and names, which is a different problem.