fix(android): new session bottom sheet follows IME keyboard

[Savlgoodman]

Problem

On Android, when creating a new session and tapping the project/path or worktree row, a bottom sheet opens with a TextInput. The auto-focused text field triggers the software keyboard, but the bottom sheet (rendered inside RNModal) stays anchored to the physical screen bottom — the keyboard covers the input field, the Done button, and the lower portion of the picker list. The screen-level KeyboardAvoidingView cannot help because RNModal lives in a separate native surface.

Fix

Make the Android branch of BottomSheet keyboard-aware by leveraging useReanimatedKeyboardAnimation from react-native-keyboard-controller (already a project dependency, already used in AgentContentView.ios.tsx and PlaceholderContainerView.tsx).

• Replace React Native Animated.Value with Reanimated useSharedValue for the sheet slide transform
• Read live IME height via useReanimatedKeyboardAnimation and combine it with the sheet's open/close translateY via useAnimatedStyle
• The sheet now tracks the keyboard animation continuously, staying above the IME with an 8px gap
• Replace Animated.spring (which caused a bouncy open animation that blocked input) with withTiming(200ms) for a smooth, responsive transition

No changes to iOS (presentationStyle="formSheet" handles this natively) or Web (uses inline popover).

Before：
*worktree

(picker stays visible)

After：

Files changed

• packages/happy-app/sources/app/(app)/new/index.tsx — Android BottomSheet component