feat: rewrite backend in Rust (axum)

Replace the Node/Express backend with a Rust implementation that keeps
the same REST API, MongoDB collections and Redis cache keys, so existing
users, subscriptions and progress keep working.

- axum + mongodb + redis, bcrypt and HS256 JWT compatible with old data
- RSS parsing, iTunes discovery/trending, background sync (1h / 4h)
- Docker image now builds a static Rust binary on debian-slim
- CI runs cargo tests before publishing the image
- compose uses pull_policy: always so a restart picks up the new image

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

dev.bat

@@ -21,9 +21,9 @@ echo ⚠️  Make sure MongoDB and Redis are running!
 echo.
 
 REM Start backend
-echo 🚀 Starting Backend (Express.js)...
+echo 🚀 Starting Backend (Rust)...
 cd backend
-start "Podcastic Backend" npm run dev
+start "Podcastic Backend" cmd /c "set PORT=5000&& cargo run"
 cd ..
 
 timeout /t 2 /nobreak