feat(backend): implement db helpers and postgres pool/transactor

db/db.go: TxFromContext/ContextWithTx for transaction propagation,
Querier interface (QueryRow/Query/Exec), ScanRow generic helper,
ClampLimit/ClampOffset pagination guards.

db/postgres/postgres.go: NewPool with ping validation, Transactor
backed by pgxpool (BeginTx → fn → commit/rollback), connOrTx helper
that returns the active transaction from context or falls back to pool.

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

backend/internal/db/postgres/postgres.go

@@ -0,0 +1,67 @@
+// Package postgres provides the PostgreSQL implementations of the port interfaces.
+package postgres
+
+import (
+	"context"
+	"fmt"
+
+	"github.com/jackc/pgx/v5"
+	"github.com/jackc/pgx/v5/pgxpool"
+
+	"tanabata/backend/internal/db"
+)
+
+// NewPool creates and validates a *pgxpool.Pool from the given connection URL.
+// The pool is ready to use; the caller is responsible for closing it.
+func NewPool(ctx context.Context, url string) (*pgxpool.Pool, error) {
+	pool, err := pgxpool.New(ctx, url)
+	if err != nil {
+		return nil, fmt.Errorf("pgxpool.New: %w", err)
+	}
+	if err := pool.Ping(ctx); err != nil {
+		pool.Close()
+		return nil, fmt.Errorf("postgres ping: %w", err)
+	}
+	return pool, nil
+}
+
+// Transactor implements port.Transactor using a pgxpool.Pool.
+type Transactor struct {
+	pool *pgxpool.Pool
+}
+
+// NewTransactor creates a Transactor backed by pool.
+func NewTransactor(pool *pgxpool.Pool) *Transactor {
+	return &Transactor{pool: pool}
+}
+
+// WithTx begins a transaction, stores it in ctx, and calls fn. If fn returns
+// an error the transaction is rolled back; otherwise it is committed.
+func (t *Transactor) WithTx(ctx context.Context, fn func(ctx context.Context) error) error {
+	tx, err := t.pool.BeginTx(ctx, pgx.TxOptions{})
+	if err != nil {
+		return fmt.Errorf("begin tx: %w", err)
+	}
+
+	txCtx := db.ContextWithTx(ctx, tx)
+
+	if err := fn(txCtx); err != nil {
+		_ = tx.Rollback(ctx)
+		return err
+	}
+
+	if err := tx.Commit(ctx); err != nil {
+		return fmt.Errorf("commit tx: %w", err)
+	}
+	return nil
+}
+
+// connOrTx returns the pgx.Tx stored in ctx by WithTx, or the pool itself when
+// no transaction is active. The returned value satisfies db.Querier and can be
+// used directly for queries and commands.
+func connOrTx(ctx context.Context, pool *pgxpool.Pool) db.Querier {
+	if tx, ok := db.TxFromContext(ctx); ok {
+		return tx
+	}
+	return pool
+}