feat: initial commit — backend API + student cabinet frontend

- Go backend: auth (JWT), points earn/spend, QR token generation,
  partners, admin grant/stats endpoints with chi router
- Next.js 14 frontend: login, student dashboard, transaction history,
  QR display, partners list
- PostgreSQL migrations (4 tables), Redis cache, Docker Compose
- CORS middleware, role-based route protection, Zustand auth store

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

backend/pkg/db/postgres.go

@@ -0,0 +1,22 @@
+// Package db provides PostgreSQL connection pool initialization.
+package db
+
+import (
+	"context"
+	"fmt"
+
+	"github.com/jackc/pgx/v5/pgxpool"
+)
+
+// NewPool creates and validates a pgx connection pool using the given DATABASE_URL.
+// Returns an error if the pool cannot be created or if the initial ping fails.
+func NewPool(ctx context.Context, databaseURL string) (*pgxpool.Pool, error) {
+	pool, err := pgxpool.New(ctx, databaseURL)
+	if err != nil {
+		return nil, fmt.Errorf("db.NewPool: create pool: %w", err)
+	}
+	if err := pool.Ping(ctx); err != nil {
+		return nil, fmt.Errorf("db.NewPool: ping: %w", err)
+	}
+	return pool, nil
+}