mahmoud-yousefi/datepicker ? reverse-engineered prompt

Build me a simple date picker app in React that lets a user open a calendar, pick a date, and see the selected date clearly on the page.

I want it to feel clean and modern, with a nice layout and basic styling, and it should work well on desktop and mobile. If it makes sense, add a way to move between months and highlight the chosen day. Keep the app easy to use, no extra clutter, just a polished date selection experience.

Use the existing React setup and Tailwind styling if that’s already in place. Please make sure it runs cleanly with the normal start command, and if you need to check current docs online for a good approach, go ahead and do that.