Fix mobile layout and add MobileDateInput

[WeixuanZ]

This PR addresses reported mobile layout issues including excessive margins below navbars and unnecessary vertical scrolling on iOS.

Changes:

1. Immersive Layout: Removed the global paddingTop: 'env(safe-area-inset-top)' from App.tsx. This was pushing all content down, creating gaps below navbars if they were intended to be immersive.
2. Scroll Fix: Removed minHeight: '100vh' from the root container in App.tsx, which can cause overflow on mobile browsers where 100vh ignores the URL bar. height: '100dvh' is sufficient.
3. Sticky Header Fix: Updated GameRoom.tsx to explicitly add safe-area padding to its sticky header (paddingTop: 'calc(16px + env(safe-area-inset-top))'), ensuring content isn't obscured by the notch while maintaining the immersive background.
4. Mobile Date Input: Added a new MobileDateInput component in frontend/src/components/MobileDateInput.tsx that wraps the native date picker with a custom, touch-friendly UI, solving the "wrong sizing" and "intuitive use" issues reported by the user.

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PR created automatically by Jules for task 5554837315683243399 started by @WeixuanZ

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