Update Android app to match iOS feature parity and perform QA testing

[typelets]

Description:
The Android app is currently behind iOS in terms of features and updates. We need to bring it up to parity with the iOS
version and perform comprehensive QA testing before release.

Current Status:

• iOS is on version X.X.X with recent updates including Public Notes, Liquid Glass UI, etc.
• Android is behind and missing recent features

Required Updates:

• Implement Public Notes feature (matching iOS functionality)
• Add PublishNoteSheet component
• Add globe icon indicators for published notes
• Add "Public" filter option
• Implement auto-sync for public notes
• Update UI/UX to match iOS where applicable
• Review and apply any bug fixes that were implemented on iOS

QA Testing Checklist:

• Authentication flows (sign up, sign in, logout)
• Note creation, editing, and deletion
• Folder management and organization
• Public notes publishing/unpublishing
• Offline mode and sync
• File attachments
• Search functionality
• Cache management
• Performance testing
• Memory leak testing
• Different Android versions compatibility
• Different screen sizes and orientations

Platform:
Android

Priority:
High - Need to maintain feature parity across platforms

Labels: enhancement, android, QA, testing