Replace the native HTML5 date input (hidden <input type="date"> with
showPicker()) with a proper shadcn/ui date picker using Calendar and
Popover components. The new implementation provides:
- Calendar popup with month navigation and keyboard support
- Clear date button in the popover footer
- Calendar icon in the trigger button
- Proper date parsing via parseDateValue helper
Also adds the design file design/date-picker-shadcn.pen with closed
and open state frames.
Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>
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