fix(android): keep composer synchronized with IME

[duoyi88]

Closes #194

Root cause

On edge-to-edge Android, adjustResize no longer moves the composer above the IME. The KeyboardAvoidingView change proposed in #182 improves the layout, but a physical Pixel 11 Pro test still left the input partially covered.

A larger keyboardVerticalOffset can correct the open position, but React Native 0.81.5 handles Android keyboardDidHide as another frame-change event. With a non-zero offset, that leaves stale bottom padding after the IME closes, so the composer does not return to the bottom.

Change

• Preserve the existing iOS KeyboardAvoidingView padding behavior and 90 dp offset.
• On Android, initialize from Keyboard.metrics(), subscribe to keyboardDidShow / keyboardDidHide, and apply the IME-reported height directly as bottom padding.
• Reset Android padding explicitly to zero on hide.
• Subscribe before resynchronizing native metrics so an IME transition during route mount cannot be lost.
• Add regression coverage for show, hide, invalid metrics, iOS isolation, and the measured Pixel geometry.

Physical-device verification

Pixel 11 Pro, Android 17:

• Play v0.4.15 reproduced Android: chat input hidden behind keyboard #194 with both Gboard and a custom Trime IME.
• The fix: keyboard/composer (#156), auto-scroll (#155), dead SSE (#186), blocked SSE startup (#189), stale transcripts, uncopyable text, axis-perfect table scrolling, 50-session list cap, transcript flash, dark-mode contrast #182-style build moved the composer but still left 106 px of the input behind the IME.
• The first complete-header-offset build fixed opening but exposed stale padding after keyboard dismissal.
• The final APK was installed over the side-by-side test package and verified by the reporter: opening the IME keeps the full composer visible; dismissing it returns the composer to the bottom.

Verification

• npm test — 339 passed
• npm run typecheck
• Keyboard offset tests — 6 passed
• Android arm64 release APK build
• Physical Pixel 11 Pro open/close cycle

The change is limited to the session keyboard integration and its small pure helper/tests.