feat: 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/db.go

@@ -0,0 +1,70 @@
+// Package db provides shared helpers used by all database adapters.
+package db
+
+import (
+	"context"
+	"fmt"
+
+	"github.com/jackc/pgx/v5"
+	"github.com/jackc/pgx/v5/pgconn"
+)
+
+// txKey is the context key used to store an active transaction.
+type txKey struct{}
+
+// TxFromContext returns the pgx.Tx stored in ctx by the Transactor, along
+// with a boolean indicating whether a transaction is active.
+func TxFromContext(ctx context.Context) (pgx.Tx, bool) {
+	tx, ok := ctx.Value(txKey{}).(pgx.Tx)
+	return tx, ok
+}
+
+// ContextWithTx returns a copy of ctx that carries tx.
+// Called by the Transactor before invoking the user function.
+func ContextWithTx(ctx context.Context, tx pgx.Tx) context.Context {
+	return context.WithValue(ctx, txKey{}, tx)
+}
+
+// Querier is the common query interface satisfied by both *pgxpool.Pool and
+// pgx.Tx, allowing repo helpers to work with either.
+type Querier interface {
+	QueryRow(ctx context.Context, sql string, args ...any) pgx.Row
+	Query(ctx context.Context, sql string, args ...any) (pgx.Rows, error)
+	Exec(ctx context.Context, sql string, args ...any) (pgconn.CommandTag, error)
+}
+
+// ScanRow executes a single-row query against q and scans the result using
+// scan. It wraps pgx.ErrNoRows so callers can detect missing rows without
+// importing pgx directly.
+func ScanRow[T any](ctx context.Context, q Querier, sql string, args []any, scan func(pgx.Row) (T, error)) (T, error) {
+	row := q.QueryRow(ctx, sql, args...)
+	val, err := scan(row)
+	if err != nil {
+		var zero T
+		if err == pgx.ErrNoRows {
+			return zero, fmt.Errorf("%w", pgx.ErrNoRows)
+		}
+		return zero, fmt.Errorf("ScanRow: %w", err)
+	}
+	return val, nil
+}
+
+// ClampLimit enforces the [1, max] range on limit, returning def when limit
+// is zero or negative.
+func ClampLimit(limit, def, max int) int {
+	if limit <= 0 {
+		return def
+	}
+	if limit > max {
+		return max
+	}
+	return limit
+}
+
+// ClampOffset returns 0 for negative offsets.
+func ClampOffset(offset int) int {
+	if offset < 0 {
+		return 0
+	}
+	return offset
+}