Fix MongoDB connection timeout on Vercel serverless

[rxmox]

Summary

• Extracts shared DB connection logic into src/utils/db.ts with ping-based stale connection detection. When Vercel freezes/thaws a serverless function, the MongoDB connection can appear connected (readyState === 1) but have a dead TCP socket. The new connectDB() pings the DB to verify liveness and reconnects if stale.
• Moves DB middleware before route handlers in app.ts. Previously, api/index.ts registered the connectDB middleware after importing app (which already had all routes mounted), so routes fired before the DB check ran. Now ensureConnection is registered on /api in app.ts before any route mounts.
• Simplifies api/index.ts to just eagerly call connectDB() at module load (for Vercel cold starts) and export app. All connection logic and middleware now lives in utils/db.ts and app.ts.
• Tunes connection options for serverless: bufferCommands: false (fail fast instead of buffering for 10s), maxPoolSize: 5, heartbeatFrequencyMS: 10000.

Problem

After ~3 days without redeployment, all DB operations fail with:

MongooseError: Operation users.findOne() buffering timed out after 10000ms

Redeploying temporarily fixes it. Root cause: Vercel freezes serverless functions between invocations, leaving stale MongoDB connections that pass the readyState check but can't actually send queries.

Files changed

File	Change
src/utils/db.ts	New: shared connectDB() with ping health check + ensureConnection middleware
src/app.ts	Register ensureConnection middleware before route handlers
api/index.ts	Simplified to eager connect + export (removed inline connection logic)
src/server.ts	Use shared connectDB() instead of direct mongoose.connect()

Test plan

• TypeScript compiles without errors
• Dev server starts and connects to MongoDB
• GET / returns Hello (no DB middleware on non-API routes)
• POST /api/auth/login queries DB successfully (returns "Invalid credentials", not a timeout)
• GET /api/users returns full user list from MongoDB
• After deploying to Vercel, monitor logs for stale connection recovery and confirm login works after 3+ days without redeployment