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>

backend/package.json

@@ -1,45 +0,0 @@
-{
-  "name": "podcastic-backend",
-  "version": "1.0.0",
-  "description": "Podcastic - Multi-user podcast streaming application backend",
-  "main": "dist/index.js",
-  "scripts": {
-    "dev": "tsx watch src/index.ts",
-    "build": "tsc",
-    "start": "node dist/index.js",
-    "lint": "eslint src",
-    "test": "vitest"
-  },
-  "keywords": ["podcast", "streaming", "audio"],
-  "author": "",
-  "license": "MIT",
-  "dependencies": {
-    "express": "^4.18.2",
-    "mongoose": "^7.5.0",
-    "redis": "^4.6.11",
-    "jsonwebtoken": "^9.0.0",
-    "bcryptjs": "^2.4.3",
-    "dotenv": "^16.3.1",
-    "cors": "^2.8.5",
-    "zod": "^3.22.4",
-    "rss-parser": "^3.12.0",
-    "axios": "^1.5.0",
-    "node-cron": "^3.0.3",
-    "helmet": "^7.1.0",
-    "express-rate-limit": "^7.1.5"
-  },
-  "devDependencies": {
-    "@types/express": "^4.17.20",
-    "@types/node": "^20.8.0",
-    "@types/cors": "^2.8.17",
-    "@types/jsonwebtoken": "^9.0.4",
-    "@types/bcryptjs": "^2.4.2",
-    "@types/node-cron": "^3.0.11",
-    "typescript": "^5.2.2",
-    "tsx": "^4.1.0",
-    "eslint": "^9.18.0",
-    "@eslint/js": "^9.18.0",
-    "typescript-eslint": "^8.22.0",
-    "vitest": "^0.34.6"
-  }
-}