feat(account): stamp last-login time + IP on cold app-load

The profile GET (fetched once per cold app-load by the SPA) stamps accounts
.last_login_at/.last_login_ip, throttled to at most once per hour per account
(best-effort, never blocks the read). IP from the gateway-forwarded X-Forwarded-For.
Feeds the account-deletion dossier. Integration test covers the throttle.

backend/internal/account/retention.go

@@ -6,6 +6,7 @@ import (
 	"fmt"
 	"time"
 
+	"github.com/go-jet/jet/v2/postgres"
 	"github.com/google/uuid"
 
 	"scrabble/backend/internal/postgres/jet/backend/table"
@@ -41,3 +42,24 @@ func retainIdentityTx(ctx context.Context, tx *sql.Tx, accountID uuid.UUID, kind
 	}
 	return nil
 }
+
+// StampLastLogin records the account's last cold-load time and client IP, but only when
+// the stored value is missing or older than an hour — so it costs at most one write per
+// account per hour (its caller, the profile fetch, runs once per cold app-load). It is a
+// best-effort audit signal that feeds the account-deletion dossier.
+func (s *Store) StampLastLogin(ctx context.Context, accountID uuid.UUID, ip string) error {
+	now := time.Now().UTC()
+	upd := table.Accounts.UPDATE(table.Accounts.LastLoginAt, table.Accounts.LastLoginIP).
+		SET(postgres.TimestampzT(now), postgres.String(ip)).
+		WHERE(
+			table.Accounts.AccountID.EQ(postgres.UUID(accountID)).
+				AND(
+					table.Accounts.LastLoginAt.IS_NULL().
+						OR(table.Accounts.LastLoginAt.LT(postgres.TimestampzT(now.Add(-time.Hour)))),
+				),
+		)
+	if _, err := upd.ExecContext(ctx, s.db); err != nil {
+		return fmt.Errorf("account: stamp last login %s: %w", accountID, err)
+	}
+	return nil
+}