Add dbx library: PostgreSQL cluster with master/replica routing, retry, health checking

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

doc.go

@@ -0,0 +1,49 @@
+// Package dbx provides a production-ready PostgreSQL helper library built on top of pgx/v5.
+//
+// It manages connection pools, master/replica routing, automatic retries with
+// exponential backoff, load balancing across replicas, background health checking,
+// and transaction helpers.
+//
+// # Quick Start
+//
+//	cluster, err := dbx.NewCluster(ctx, dbx.Config{
+//	    Master: dbx.NodeConfig{
+//	        Name: "master",
+//	        DSN:  "postgres://user:pass@master:5432/mydb",
+//	        Pool: dbx.PoolConfig{MaxConns: 20, MinConns: 5},
+//	    },
+//	    Replicas: []dbx.NodeConfig{
+//	        {Name: "replica-1", DSN: "postgres://...@replica1:5432/mydb"},
+//	    },
+//	})
+//	if err != nil {
+//	    log.Fatal(err)
+//	}
+//	defer cluster.Close()
+//
+//	// Write → master
+//	cluster.Exec(ctx, "INSERT INTO users (name) VALUES ($1)", "alice")
+//
+//	// Read → replica with fallback to master
+//	rows, _ := cluster.ReadQuery(ctx, "SELECT * FROM users WHERE active = $1", true)
+//
+//	// Transaction → master, panic-safe
+//	cluster.RunTx(ctx, func(ctx context.Context, tx pgx.Tx) error {
+//	    _, _ = tx.Exec(ctx, "UPDATE accounts SET balance = balance - $1 WHERE id = $2", 100, fromID)
+//	    _, _ = tx.Exec(ctx, "UPDATE accounts SET balance = balance + $1 WHERE id = $2", 100, toID)
+//	    return nil
+//	})
+//
+// # Routing
+//
+// The library uses explicit method-based routing (no SQL parsing):
+//   - Exec, Query, QueryRow, Begin, BeginTx, CopyFrom, SendBatch → master
+//   - ReadQuery, ReadQueryRow → replicas with master fallback
+//   - Master(), Replica() → direct access to specific nodes
+//
+// # Retry
+//
+// Retryable errors include connection errors (PG class 08), serialization failures (40001),
+// deadlocks (40P01), and too_many_connections (53300). A custom classifier can be provided
+// via RetryConfig.RetryableErrors.
+package dbx