fix: Fix Docker build for public directory

- Update Dockerfile to ensure public directory exists in builder stage
- Use 'COPY /app/public/. ./public/' pattern for robust copying
- Add manifest.json to public folder (non-empty directory)
- Remove .gitkeep placeholder

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

public/.gitkeep

@@ -1 +0,0 @@
-

public/manifest.json

@@ -0,0 +1 @@
+{"name":"letsbe-hub"}