fix: disable catch_up replay to prevent message loss

Catch-up was replaying all server messages on every reconnect,
causing duplicate assistant messages and overwriting user messages.
Local storage is now the source of truth. Catch-up only updates
lastSeq for protocol tracking. New messages while offline are
stored via _storeForSession from the DIRECT broadcast path.

Also: SharedPreferences save awaited properly, image cache for
flicker prevention, screenshot snackbar indicator.

lib/screens/chat_screen.dart

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